Antonella Marchesiello (Czech Technical University, Prague)
Symmetric resonances and bifurcations in Hamiltonian systems
We consider the problem of determining the orbit structure of two degrees of freedom Hamiltonian systems describing symmetric resonances. More precisely, we investigate the phase-space structure of Hamiltonian systems with positive definite quadratic part, close to an equilibrium and invariant under spatial reflection symmetries and time reversion symmetry. The analysis is performed combining three different mathematical tools: Perturbation Theory, Normal Forms Theory and Singularity Theory. We study the most relevant resonances and related bifurcations providing quantitative predictions, in the form of energy threshold values, which determine the appearance of the main periodic orbits (joint work with Giuseppe Pucacco).