A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems.

Creators: Guzzo, Massimiliano; Lega, Elena; Froeschle, Claude

Others:: Dipartimento di Matematica Pura e Applicata [Padova] ; Università degli Studi di Padova = University of Padua (Unipd); Laboratoire de Cosmologie, Astrophysique Stellaire & Solaire, de Planétologie et de Mécanique des Fluides (CASSIOPEE) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Description

We investigate numerically the stable and unstable manifolds of the hyperbolic manifolds of the phase space related to the resonances of quasi-integrable systems in the regime of validity of the Nekhoroshev and KAM theorems. Using a model of weakly interacting resonances we explain the qualitative features of these manifolds characterized by peculiar 'flower--like' structures. We detect different transitions in the topology of these manifolds related to the local rational approximations of the frequencies. We find numerically a correlation among these transitions and the speed of Arnold diffusion.

A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi--integrable systems.

Description

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