Rijksuniversiteit Groningen
-

-Department of Mathematics and Computing Science
-Staff

+F.Takens


-Affiliation
-Professional biography
-Onderwijs (dutch only)
-Research
-Other information


Head of page Affiliation

Naam

University of Groningen, Department of Mathematics
P.O. Box 407, 9700 AK Groningen, The Netherlands
Tel: +31 (0)50 3633939 (secretary)
Fax: +31 (0)50 3633800
E-mail:F.Takens@rug.nl

Head of page Professional biography

Prof. dr. F. Takens studied mathematics at the University of Amsterdam where he obtained his Ph.D. degree in 1969. Since 1972 he is appointed as a full professor at the University of Groningen. He is editor of the Springer Lecture Notes in Mathematics and member of the Royal Netherlands Academy of Arts and Sciences (KNAW)

Head of page Onderwijs

Head of page Research

Keywords

Description

Research is concentrated on two main themes: transitions to chaotic dynamics and analysis of time series.

Transitions to chaotic dynamics are part of bifurcation theory, and are aimed at supporting mathematical interpretations of experimentally observed transistions between regular and chaotic behaviour (like the transition from laminar to turbulent flow in fluid dynamics). Mainly transitions related to homoclinic tangencies were studied recently.

The interest in time series analysis was initiated by the question how to distinguish deterministic chaos from stochasticity in experimental time series. Also, more generally, the question is addressed how to distinguish different time series, possibly from deterministic but chaotic systems, in cases where this is not possible with methods based on the power spectrum.

For more details on the research in dynamical systems at the University of Groningen click here

Selected publications

  1. D. Ruelle, F. Takens, On the nature of tubulence, Comm. Math. Phys. 20 (1971), 167-192.

  2. F. Takens, Homoclinic points of conservative systems, Inv. Math. 18 (1972), 267-292.

  3. F. Takens, Singularities of vector fields, Publ. IHES 43 (1974), 47-100.

  4. F. Takens, Constrained equations; a study of implicit differential equations and their discontinuous solutions, in: Structural stability, the theory of catastrophes, and applications in the sciences, LNM 525, Springer-Verlag, 1976.

  5. F. Takens, A global version of the inverse problem of the calculus of variations, J. Diff. Geom. 14 (1979), 543-562.

  6. F. Takens, Detecting strange attractors in turbulence, in: Dynamical systems and turbulence-Warwick 1980, LNM 898, Springer-Verlag, 1981.

  7. S. Newhouse, J. Palis, F. Takens, Bifurcations and stability of families of diffeomorphisms, Publ. IHES 57 (1983), 5-71.

  8. J. Palis, F. Takens, Stability of parametrized families of gradient vector fields, Ann. Math. 118 (1983), 383-421.

  9. F. Takens, Moduli of stability for gradients, in: Singularities and dynamical systems, ed. S. N. Pnevmatikos, North-Holland, 1985.

  10. J. Palis, F. Takens, Hyperbolicity and the creation of homoclinic orbits, Ann. Math. 125 (1987), 337-374.

  11. H. W. Broer, F. Takens, Formally symmetric normal forms and genericity, in: Dynamics reported 2 (1989), 39-60.

  12. F. Takens, Adundance of generic homoclinic tangencies in real-analytic families of diffeomorphisms, Bol. Soc. Bras. Mat., 22 (1992), 191-214.

  13. J. Palis, F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993, x + 234 p.

  14. J. S. Schouten, F. Takens, C. M. van den Bleek, Maximum-likelihood estimation of the entropy of an attractor, Phys. Rev. E 49 (1994) 126 - 129.

  15. F.Takens, Heteroclinic attractors: time averages and moduli of topological conjugacy, Bol. Soc. Bras. Mat. 25 (1994), 107 - 120.

  16. C. Diks, J. C. van Houwelingen, F. Takens, J. DeGoede, Reversibility as a criterion for discriminating time series, Phys. Lett. A 201 (1995), 221 - 228.

Head of page Other information



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Last update: Jan 19, 1999