Orateur
Description
This work studies conformally symplectic diffeomorphisms defined in a symplectic manifold, that is, diffeomorphisms which transform a symplectic form into a multiple of itself, through a conformal factor.
We focus on Normally hyperbolic invariant manifolds (NHIM) and their (un)stable manifolds, which are important landmarks that organize long-term dynamical behaviorb
We prove that a NHIM is symplectic if and only if the rates of hyperbolicity satisfy certain pairing rules and if and only if the rates and the conformal factor satisfy certain (natural) inequalities.
Homoclinic excursions to NHIMs are quantitatively described by scattering maps, which give the trajectory asymptotic in the future as a function of the trajectory asymptotic in the past.
We prove that the scattering map is symplectic even if the dynamics is dissipative.
We also show that if the symplectic form is exact, then the scattering maps are exact, even if the dynamics is not exact.
