Robustly non-hyperbolic transitive symplectic dynamics

TL;DR

This paper constructs symplectic dynamical systems in higher dimensions that exhibit robust transitivity and complex tangencies, advancing understanding of stability and chaos in symplectic geometry.

Contribution

It introduces new symplectomorphisms with semi-local robust transitivity and homoclinic tangencies of arbitrary codimension in dimensions four and higher.

Findings

Existence of symplectomorphisms with robust transitivity in dimension ≥ 4

Construction of systems with homoclinic tangencies of any codimension c

Extension of dynamical complexity in symplectic settings

Abstract

We construct symplectomorphisms in dimension $d\geq 4$ having a semi-local robustly transitive partially hyperbolic set containing $C^2$-robust homoclinic tangencies of any codimension $c$ with $0<c\leq d/2$.