Johann Bernoulli Stichting voor de Wiskunde te Groningen

Floris Takens 1940-2010

Floris Takens (Zaandam 12 November 1940 - Groningen 10 Juni 2010) was a professor at the University of Groningen between 1972 and 1999.

[Portrait by Jacqueline Kasemier]

Floris Takens werd op 12 November 1940 in Zaandam geboren als derde van vier kinderen. Zijn ouders, Willy Bremmer en Pieter Roelf Takens, doceerden beiden klassieke talen. Floris had twee broers, Henk en Roelf, en een zuster, Leida. Hij werd genoemd naar zijn oom Floris Bremmer die in Den Haag woonde. Bremmer was op zijn beurt genoemd naar de schilder Floris Verster die een collega en goede vriend was van zijn grootvader H.P. Bremmer, ''de kunstpaus'’. Van de laatste bezat Takens een schilderij dat hij nagelaten heeft aan het Kröller-Müller museum.

In zijn jeugd ontwikkelde hij een grote passie voor de dwarsfluit, later traverso. Floris Takens trouwde in 1965 met Janna Vera Dijk en in 1967 werd hun dochter Els geboren. Het huwelijk eindigde in 1993.

Hij stierf op 20 juni 2010 te Groningen op de leeftijd van 69 jaar. Hij ligt begraven op het kerkhof van Bedum, het dorp waar hij de laatste 20 jaar van zijn leven gewoond heeft. Zijn mede-redacteur Bernard Teissier van de Springer Lecture Notes in Dynamical Systems, prees Takens in zijn condoleance om diens “immense culture”.

Studie en carrière. Takens’ studie aan de Universiteit van Amsterdam begon in 1959 en werd afgesloten met een promotie bij Nicolaas Hendrik Kuiper (1920-1994) op het proefschrift The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category. Van 1972 tot 1999 was Floris Takens hoogleraar “Differentiaaltopologie in het bijzonder Dynamische Systemen” aan de Rijksuniversiteit Groningen.

De toevoeging “in het bijzonder Dynamische Systemen” ontstond naar aanleiding van een bezoek aan het Institut des Hautes Études Scientifiques in Bures-sur-Yvette nabij Parijs, waar hij invloeden onderging van René Thom en David Ruelle. Met de laatste schreef hij het baanbrekende artikel "On the nature of turbulence", gepubliceerd in het tijdschrift Communications of Mathematical Physics. Dit artikel legt een verband tussen `turbulentie' en het toen recent onstane begrip `chaos'.

Zodoende kwam hij in contact met de Braziliaan Jacob Palis (1940- ), gepromoveerd bij Stephen Smale (1930- ). Takens en Palis hebben vanaf 1971 een vruchtbare wetenschappelijke samenwerking onderhouden. In 1991 trad Takens toe tot de KNAW. Veel eerder was hij al lid geworden van de Braziliaanse Academie.

Onderzoeksthema’s. Grofweg valt het werk van Takens uiteen in een tweetal richtingen. In beide richtingen samen heeft hij een twintigtal promovendi gehad.

Stabiliteit, hyperboliciteit, bifurcaties. Met zijn onderzoek aan structurele stabiliteit, moduli en dergelijke in de context van (bijna) hyperboliciteit en aan de bifurcaties van eenvoudig naar complexe dynamica behoort Takens tot de grondleggers van het moderne vakgebied dynamische systemen. Promovendi in deze richting zijn de Groningers Albert Hummel, Henk Broer, Gert Vegter, Fopke Klok, Jan Barkmeijer, Cars Hommes, Ale Jan Homburg, Bernd Krauskopf, Florian Wagener, Evgeny Verbitskiy en Renato Vitolo. Buiten Groningen zijn daaraan toe te voegen Freddy Dumortier, Bert Jongen en Sebastian van Strien.

Niet-lineaire tijdreeksen. Rond 1980 sloeg Takens een nieuwe richting in, waarbij uit tijdreeksen van deterministische systemen, waarvan de bewegingsvergelijkingen niet bekend hoeven te zijn, toch informatie wordt gewonnen over karakteristieken van de dynamica, zoals dimensies van attractoren, entropie, Lyapunov exponenten, etc. Vele niet-wiskundigen hebben deze theorie, inmiddels "Takens reconstructietheorie" geheten, gebruikt en aangepast voor hun doeleinden. Zijn bijdragen aan de chemische procestechnologie hebben hem een Delfts eredoctoraat opgeleverd. Promovendi in deze onderzoeksrichting zijn Jan-Pieter Pijn, Pieter Been, Cees Diks en Marcel van der Heijden.

GRAF met twee LEGPUZZELBEWIJZEN van de STELLING van PYTHAGORAS
vergelijk ook de bovenhoeken van het academieportret

Na zijn emeritaat was Takens nog betrokken bij de promoties van Renato Vitolo en Olga Lukina. De eerste hiervan betreft de complexe dynamica van klimaatmodellen en de tweede de meetkunde (onder meer Chernse klassen) van torus bundels in integreerbare Hamilton systemen.

Literatuur over F. Takens:

Publicaties van F. Takens:

[1] Takens, F., Isolated critical points of $C^\infty$ and $C^\omega$ functions. Indag. Math. 29 (1967), 238-243.
[2] Takens, F., The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category. Invent. Math. 6 (1968), 197-244.
[3] Takens, F., On the differential forms, representing the Chern and Euler classes. Rev. Roumaine Math. Pures Appl. 14 (1969), 693-702.
[4] Takens, F., Hamiltonian systems: Generic properties of closed orbits and local perturbations. Math. Ann. 188 (1970), 304-312.
[5] Takens, F., The Lusternik-Schnirelman categories of a product space. Compositio Math. 22 1970, 175-180.
[6] Takens, F., On Zeeman's tolerance stability conjecture. Manifolds—Amsterdam 1970 (Proc. Nuffic Summer School). Lecture Notes in Mathematics 197 (1971), 209-219.
[7] Ruelle, D. and F. Takens, On the nature of turbulence. Comm. Math. Phys. 20 1971 167-192.
[8] Ruelle, D. and F. Takens, Note concerning our paper: "On the nature of turbulence". Comm. Math. Phys. 23 (1971), 343-344.
[9] Takens, F. and J. White, Morse theory of double normals of immersions. Indiana Univ. Math. J. 21 1971/1972 11-17.
[10] Takens, F., A note on sufficiency of jets. Invent. Math. 13 (1971), 225-231.
[11] Takens, F., A $C^1$ counterexample to Moser's twist theorem. Indag. Math. 33 (1971), 378-386.
[12] Takens, F., Partially hyperbolic fixed points. Topology 10 (1971), 133-147.
[13] Klingenberg, W. and F. Takens, Generic properties of geodesic flows. Math. Ann. 197 (1972), 323-334.
[14] Takens, F., Singularities of functions and vectorfields. Nieuw Arch. Wisk. (3) 20 (1972), 107-130.
[15] Takens, F., Some remarks on the Böhme-Berger bifurcation theorem. Math. Z. 129 (1972), 359-364.
[16] Takens, F., Homoclinic points in conservative systems. Invent. Math. 18 (1972), 267-292.
[17] Takens, F., Derivations of vector fields. Compositio Math. 26 (1973), 151-158.
[18] Takens, F., Integral curves near mildly degenerate singular points of vector fields. Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) (1973) 599-617. Academic Press.
[19] Takens, F., Unfoldings of certain singularities of vectorfields: generalized Hopf bifurcations. J. Differential Equations 14 (1973), 476-493.
[20] Takens, F., A nonstabilizable jet of a singularity of a vector field. Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) (1973), 583-597. Academic Press.
[21] Takens, F., Normal forms for certain singularities of vectorfields. Colloque International sur l'Analyse et la Topologie Différentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972). Ann. Inst. Fourier (Grenoble) 23(2) (1973), 163-195.
[22] Dumortier, F. and F. Takens, Characterization of compactness for symplectic manifolds. Bol. Soc. Brasil. Mat. 4(2) (1973), 167-173.
[23] Takens, F., Singularities of vector fields. Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47-100.
[24] Takens, F., Forced oscillations and bifurcations. Applications of global analysis, I (Sympos., Utrecht State Univ., 1973). Comm. Math. Inst. Rijksuniv. Utrecht 3 (1974), 1-59
[25] Takens, F., Introduction to global analysis. Lectures held at Utrecht State University, October–December, 1972. Communications of the Mathematical Institute, Rijksuniversiteit Utrecht, 1974, iii+111 pp.
[26] Banchoff, T. and F. Takens, Height functions on surfaces with three critical points. Illinois J. Math. 19 (1975), 325-335.
[27] De la Harpe, P. and F. Takens, Examples of manifolds which are homogeneous spaces of Lie groups of arbitrarily large dimension. Manuscripta Math. 15 (1975), 275-287.
[28] Takens, F., Constrained equations; a study of implicit differential equations and their discontinuous solutions. Report ZW-75-03, Mathematisch Instituut, Rijksuniversiteit Groningen (1975), i+91 pp.
[29] Takens, F., Tolerance stability. Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E.C. Zeeman on his fiftieth birthday). Lecture Notes in Math. 468 (1975), 293-304.
[30] Takens, F., Geometric aspects of non-linear R.L.C. networks. Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E.C. Zeeman on his fiftieth birthday). Lecture Notes in Math. 468 (1975), 305-331.
[31] Newhouse, S.E., J. Palis and F. Takens, Stable arcs of diffeomorphisms. Bull. Amer. Math. Soc. 82(3) (1976), 499-502.
[32] Takens, F., and W. White, Vector fields with no nonwandering points. Amer. J. Math. 98(2) (1976), 415-425.
[33] Takens, F., Implicit differential equations; some open problems. Singularités d'applications différentiables (Sém., Plans-sur-Bex, 1975). Lecture Notes in Math. 535 (1976), 327-253.
[34] Palis, J. and F. Takens, Topological equivalence of normally hyperbolic dynamical systems. Topology 16(4) (1977), 335-345.
[35] Takens, F., Symmetries, conservation laws and variational principles. Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976). Lecture Notes in Math. 597 (1977), 581-604.
[36] Newhouse, S.E., D. Ruelle and F. Takens, Occurrence of strange Axiom A attractors near quasiperiodic flows on $\mathbb{T}^m$, $m \ge 3$. Comm. Math. Phys. 64(1) (1978/79), 35-40.
[37] Takens, F., Some remarks on Souriau's theory of elementary systems. Proceedings of the Eleventh Brazilian Mathematical Colloquium (Poços de Caldas, 1977), Vol. II. Inst. Mat. Pura Apl. (1978), 593-598.
[38] Takens, F., Singularities of vectorfields and bifurcations. Proceedings of the Tenth Brazilian Colloquium (Poços de Caldas, 1975), Vol. II. Cons. Nac. Desenvolvimento Ci. Tec., Inst. Mat. Pura Apl. (1978), 541-546.
[39] Takens, F., Global phenomena in bifurcations of dynamical systems with simple recurrence. Jahresber. Deutsch. Math.-Verein. 81(2) (1978/79), 87-96.
[40] Takens, F., Symmetries, conservation laws and symplectic structures; elementary systems. Proceedings, Bicentennial Congress Wiskundig Genootschap (Vrije Univ., Amsterdam, 1978), Part II. Math. Centre Tracts 101 (1979), 375-389.
[41] Takens, F., Characterization of a differentiable structure by its group of diffeomorphisms. Bol. Soc. Brasil. Mat. 10(1) (1979), 17-25.
[42] Takens, F., A global version of the inverse problem of the calculus of variations. J. Differential Geom. 14(4) (1979), 543-562 (1981).
[43] Takens, F., Moduli and bifurcations; nontransversal intersections of invariant manifolds of vectorfields. Functional differential equations and bifurcation (Proc. Conf., Inst. Ciênc. Mat. São Carlos, Univ. São Paulo, São Carlos, 1979). Lecture Notes in Math. 799 (1980), 368-384.
[44] Takens, F., Motion under the influence of a strong constraining force. Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979). Lecture Notes in Math. 819 (1980), 425-445.
[45] Takens, F., Detecting strange attractors in turbulence. Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980). Lecture Notes in Math. 898 (1981), 366-381.
[46] Newhouse, S.E., J. Palis and F. Takens, Bifurcations and stability of families of diffeomorphisms. Inst. Hautes Études Sci. Publ. Math. 57 (1983), 5-71.
[47] Palis, J. and F. Takens, Stability of parametrized families of gradient vector fields. Ann. of Math. (2) 118(3) (1983), 383-421.
[48] Takens, F., Distinguishing deterministic and random systems. Nonlinear dynamics and turbulence, Interaction Mech. Math. Ser., Pitman (1983), 314-333.
[49] Takens, F., Mechanical and gradient systems; local perturbations and generic properties. Bol. Soc. Brasil. Mat. 14(2) (1983), 147-162.
[50] Takens, F., Moduli of singularities of vector fields. Topology 23(1) (1984), 67-70.
[51] Bamón, R., I.P. Malta, M.J. Pacífico and F. Takens, Rotation intervals of endomorphisms of the circle. Ergodic Theory Dynam. Systems 4(4) (1984), 493-498.
[52] Takens, F., A nonstabilizable jet of a singularity of a vector field: the analytic case. Algebraic and differential topology — global differential geometry. Teubner-Texte Math. 70 (1984) 288-305.
[53] Broer, H.W., B.L.J. Braaksma and F. Takens (eds.), Dynamical Systems and Bifurcations. Lecture Notes in Math. 1125 1985.
[54] Takens, F., On the numerical determination of the dimension of an attractor. Dynamical systems and bifurcations (Groningen, 1984). Lecture Notes in Math. 1125 (1985), 99-106.
[55] Takens, F., Moduli of stability for gradients. Singularities and dynamical systems (Ir áklion, 1983). North-Holland Math. Stud. 103 (1985) 69-79.
[56] Takens, F., Singularities of gradient vector fields and moduli. Singularities and dynamical systems (Ir áklion, 1983). North-Holland Math. Stud. 103 (1985), 81-88.
[57] Palis, J. and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms. Invent. Math. 82(3) (1985), 397-422.
[58] Takens, F., A note on the differentiability of centre manifolds. Dynamical systems and partial differential equations (Caracas, 1984). Univ. Simon Bolivar, Caracas (1986), 101-104.
[59] Palis, J. and F. Takens, Hyperbolicity and the creation of homoclinic orbits. Ann. of Math. (2) 125(2) (1987), 337-374.
[60] Takens, F., Transitions from periodic to strange attractors in constrained equations. Dynamical systems and bifurcation theory (Rio de Janeiro, 1985). Pitman Res. Notes Math. Ser. 160 (1987), 399-421.
[61] Takens, F., Homoclinic bifurcations. Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) 1 (2) (1987), 1229-1236.
[62] Palis, J. and F. Takens, Homoclinic bifurcations and hyperbolic dynamics. 16o Colóquio Brasileiro de Matem ática. [16th Brazilian Mathematics Colloquium] Instituto de Matem ática Pura e Aplicada (IMPA), Rio de Janeiro, 1987. iv+134 pp.
[63] Takens, F., Limit capacity and Hausdorff dimension of dynamically defined Cantor sets. Dynamical systems, Valparaiso 1986, Lecture Notes in Math. 1331 (1988), 196-212.
[64] Takens, F., Intermittency: global aspects. Dynamical systems, Valparaiso 1986, Lecture Notes in Math. 1331 (1988), 213-239.
[65] Takens, F., Measure and category. Singularities (Warsaw, 1985). Banach Center Publ. 20 (1988), 411-418.
[66] Broer, H.W. and F. Takens, Formally symmetric normal forms and genericity. Dynamics Reported (N.S.) 2 (1989), 39-59.
[67] Takens, F., On Poincaré's geometric investigations of the equations of classical mechanics. Bull. Soc. Math. Belg. Sér. A 41(1) (1989), 37-50.
[68] Broer, H.W., G.B. Huitema, F. Takens and B.L.J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori. Mem. Amer. Math. Soc. 83(421) (1990), viii+175 pp.
[69] Takens, F., Homoclinic bifurcations. Workshop on Dynamical Systems (Trieste, 1988). Pitman Res. Notes Math Ser. 221 (1990), 53-58.
[70] Broer, H.W. and F. Takens, Wegen naar chaos en vreemde aantrekking, een fenomenologische benadering. Dynamische Systemen en Chaos, een Revolutie vanuit de Wiskunde. Epsilon-Uitgaven 14 (1990), 1-76.
[71] Broer, H.W., F. Dumortier, S.J. van Strien and F. Takens, Structures in dynamics. Finite-dimensional deterministic studies. Studies in Mathematical Physics 2. North-Holland, 1991. xii+309 pp.
[72] Takens, F., Deterministic dynamical systems and chaos. Mathematische Wissenschaften gestern und heute. 300 Jahre Mathematische Gesellschaft in Hamburg, Teil 4 (Hamburg, 1990). Mitt. Math. Ges. Hamburg 12(4) (1992), 1049-1057.
[73] Broer, H.W. and F. Takens (eds.), Geometry and analysis in nonlinear dynamics (Groningen, 1989). Pitman Res. Notes Math. Ser. 222 1992.
[74] Takens, F., On the geometry of nontransversal intersections of invariant manifolds and scaling properties of bifurcation sets. Geometry and analysis in nonlinear dynamics (Groningen, 1989). Pitman Res. Notes Math. Ser. 222 (1992), 70-84.
[75] Takens, F., Abundance of generic homoclinic tangencies in real-analytic families of diffeomorphisms. Bol. Soc. Brasil. Mat. (N.S.) 22(2) (1992), 191-214.
[76] Stojanov, L. and F. Takens, Generic properties of closed geodesics on smooth hypersurfaces. Math. Ann. 296(3) (1993), 385-402.
[77] Takens, F., Detecting nonlinearities in stationary time series. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 3(2) (1993), 241-256.
[78] Broer, H.W. and F. Takens, Mixed spectra and rotational symmetry. Arch. Rational Mech. Anal. 124(1) (1993), 13-42.
[79] Posthumus, R.A. and F. Takens, Homoclinic tangencies: moduli and topology of separatrices. Ergodic Theory Dynam. Systems 13(2) (1993), 369-385.
[80] Palis, J. and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations. Fractal dimensions and infinitely many attractors. Cambridge Studies in Advanced Mathematics 35, 1993.
[81] Takens, F., The work of Professor Sir Christopher Zeeman FRS. Nieuw Arch. Wisk. (4) 11(3) (1993), 251-256.
[82] Takens, F., Heteroclinic attractors: time averages and moduli of topological conjugacy. Bol. Soc. Brasil. Mat. (N.S.) 25(1) (1994), 107-120.
[83] Schouten, J.C., F. Takens and C.M. van den Bleek, Maximum-likelihood estimation of the entropy of an attractor. Phys. Rev. E (3) 49(1) (1994), 126-129.
[84] Schouten, J.C., F. Takens and C.M. van den Bleek, Estimation of the dimension of a noisy attractor. Phys. Rev. E (3) 50(3) (1994), 1851-1861.
[85] Takens, F., Reduction entropy. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5(2) (1995), 585-593.
[86] Diks, C., W.R. van Zwet, F. Takens and J. DeGoede, Detecting differences between delay vector distributions. Phys. Rev. E (3) 53(3) (1996), 2169-2176.
[87] Broer, H.W., S.A. van Gils, I. Hoveijn and F. Takens (eds.), Nonlinear dynamical systems and chaos (Groningen, 1995), Pitman Progr. Nonlinear Differential Equations Appl. 19 1996.
[88] Takens, F., Estimation of dimension and order of time series. Nonlinear dynamical systems and chaos (Groningen, 1995), Progr. Nonlinear Differential Equations Appl. 19 (1996), 405-422.
[89] Takens, F., The effect of small noise on systems with chaotic dynamics. Stochastic and spatial structures of dynamical systems (Amsterdam, 1995). Konink. Nederl. Akad. Wetensch. Verh. Afd. Natuurk. Eerste Reeks 45 (1996), 3-15.
[90] Diks, C., F. Takens and J. DeGoede, Spatio-temporal chaos: a solvable model. Phys. D 104(3-4) (1997), 269-285.
[91] Bakker, R., R.J. Korte, J.C. Schouten, C.M. van den Bleek and F. Takens, Neural networks for prediction and control of chaotic fluidized bed hydrodynamics: a first step. Fractals 5(3) (1997), 523-530.
[92] Takens, F., Chaos in systems beyond hyperbolicity. Tr. Mat. Inst. Steklova Din. Sist. i Smezhnye Vopr. 216 (1997), 364-369; translation in Proc. Steklov Inst. Math. 216(1) (1997), 360-365.
[93] Takens, F. and E.A. Verbitskiy, Generalized entropies. (Russian) Mat. Zametki 63(1) (1998), 127-130; translation in Math. Notes 63(1-2) (1998), 112-115.
[94] Takens, F. and E.A. Verbitskiy, Generalized entropies: Rényi and correlation integral approach. Nonlinearity 11(4) (1998), 771-782.
[95] Takens, F., The analysis of correlation integrals in terms of extremal value theory. Bol. Soc. Brasil. Mat. (N.S.) '29'''(2) (1998), 197-228.
[96] Takens, F. and E.A. Verbitskiy, Multifractal analysis of local entropies for Gibbs measures. International Conference on Dimension and Dynamics (Miskolc, 1998). Period. Math. Hungar. 37(1-3) (1998), 143-151.
[97] Takens, F. and E.A. Verbitskiy, Multifractal analysis of local entropies for expansive homeomorphisms with specification. Comm. Math. Phys. 203 (3) (1999), 593-612.
[98] Broer, H.W., F. Takens and F.O.O. Wagener, Integrable and non-integrable deformations of the skew Hopf bifurcation. Regul. Chaotic Dyn. 4(2) (1999), 16-43.
[99] Takens, F. and F.O.O. Wagener, Resonances in skew and reducible quasi-periodic Hopf bifurcations. Nonlinearity 13(2) (2000), 377-396.
[100] Maes, C., F. Redig, Takens, F., A. van Moffaert and E.A. Verbitskiy, Intermittency and weak Gibbs states. Nonlinearity 13(5) (2000), 1681-1698.
[101] Takens, F. and E.A. Verbitskiy, General multifractal analysis of local entropies. Fund. Math. 165(3) (2000), 203-237.
[102] Takens, F. and E.A. Verbitskiy, Multifractal analysis of dimensions and entropies. Regul. Chaotic Dyn. 5(4) (2000), 361-382.
[103] Van de Craats, J. and F. Takens, De juiste toon, de juiste stemming. Nieuw Arch. Wisk. 5/2(2) (2001), 136-145.
[104] Takens, F., Forced oscillations and bifurcations. Global analysis of dynamical systems. Inst. Phys. (2001), 1-61; reprint of [24].
[105] Takens, F. and E.A. Verbitskiy, Rényi entropies of aperiodic dynamical systems. Israel J. Math. 127 (2002), 279-302.
[106] Takens, F., The reconstruction theorem for endomorphisms. Bol. Soc. Brasil. Mat. (N.S.) 33(2) (2002), 231-262.
[107] Takens, F. and E.A. Verbitskiy, On the variational principle for the topological entropy of certain non-compact sets. Ergodic Theory Dynam. Systems 23(1) (2003), 317-348.
[108] Van den Broek, P.L.C., J. van Egmond, C.M. van Rijn, F. Takens, A.M.L. Coenen and L.H.D.J. Booij, Feasibility of real-time calculation of correlation integral derived statistics applied to EEG time series. Phys. D 203(3-4) (2005), 198-208.
[109] Takens, F., Multiplications in solenoids as hyperbolic attractors. Topology Appl. 152(3) (2005), 219-225.
[110] Takens, F., Time series analysis: smoothed correlation integrals, autocovariances, and power spectra. EQUADIFF 2003. World Sci. Publ. (2005), 128-135.
[111] Broer, H.W. and F. Takens, Unicity of KAM tori. Ergodic Theory Dynam. Systems 27(3) (2007), 713-724.
[112] Broer, H.W., R.H. Cushman, F. Fassò and F. Takens, Geometry of KAM tori for nearly integrable Hamiltonian systems. Ergodic Theory Dynam. Systems 27(3) (2007), 725-741.
[113] Takens, F., Orbits with historic behaviour, or non-existence of averages. Nonlinearity 21(3) (2008), T33-T36.
[114] Lukina, O. V., F. Takens and H.W. Broer, Global properties of integrable Hamiltonian systems. Regul. Chaotic Dyn. 13(6) (2008), 602-644.
[115] Broer, H.W. and F. Takens, Dynamical systems and chaos. Epsilon-Uitgaven, 64, 2009.
[116] Broer, H.W., B. Hasselblatt and F. Takens (eds.), Handbook of Dynamical Systems Vol. 3. North-Holland, 2010.
[117] Takens, F., Reconstruction theory and nonlinear time series analysis. Handbook of Dynamical Systems, Vol. 3 (2010), 345-378.
[118] Broer, H.W. and F. Takens, Dynamical systems and chaos. Applied Mathematical Sciences, 172. Springer 2011.

Publicaties van F. Takens op MathSciNet

Mathematics Genealogy Project voor F. Takens

[HWB en HSVdS Augustus 2018]