Chaos detection tools in Hamiltonian dynamics

PABLO CINCOTTA; CLAUDIA GIORDANO

Madrid

Congreso; 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications-Special Session SS111: Computational dynamics in Hamiltonian and dissipative systems; 2014

Universidad Autónoma de Madrid

In this plenary talk I will discuss extensively the use of dynamical indicators that have proven to be efficient to investigate both regular and chaotic components of phase space of Hamiltonian systems. As it will be shown, they provide a clear picture of the resonance structure, the location of stable and unstable periodic orbits as well as a measure of hyperbolicity in chaotic domains which coincides with that given by the maximum Lyapunov characteristic exponent. Moreover, most dynamical indicators, based on the evolution of the so-called deviation vectors, are suitable to reveal the extremely thin chaotic layers around resonances and therefore, to investigate numerically the ?diffusion? along a single resonance (Arnold diffusion?). Applications to discrete and continuous systems will be addressed, as well as an overview of the stability studies present in the literature encompassing quite different dynamical systems will be provided.