Homoclinic tangencies and hyperbolicity for surface diffeomorphisms.
Density of hyperbolicity and tangencies in sectional dissipative regions
Robust transitivity in hamiltonian dynamics
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce open sets () of symplectic diffeomorphisms and Hamiltonian systems, exhibitingrobustly transitive sets. We show that the closure of such open sets contains a variety of systems, including so-called unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is...
Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models
We consider a family of planar systems introduced in 1991 by Benedicks and Carleson as a toy model for the dynamics of the so-called Hénon maps. We show that Smale’s Axiom A property is -dense among the systems in this family, despite the existence of -open subsets (closely related to the so-called Newhouse phenomena) where Smale’s Axiom A is violated. In particular, this provides some evidence towards Smale’s conjecture that Axiom A is a -dense property among surface diffeomorphisms. The basic...
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