Attractors and repellers near generic elliptic points of reversible maps

TL;DR

This paper demonstrates that near a generic elliptic periodic point in reversible maps, resonance zones typically contain stable and unstable periodic orbits as well as complex hyperbolic sets, revealing intricate local dynamics.

Contribution

It establishes the generic presence of stable, unstable, and hyperbolic sets near elliptic points in reversible maps, advancing understanding of local dynamical structures.

Findings

Resonance zones contain stable and unstable periodic orbits.

Wild hyperbolic sets are present near elliptic points.

Results are generic for reversible maps.

Abstract

We show that resonance zones near an elliptic periodic point of a reversible map must, generically, contain asymptotically stable and asymptotically unstable periodic orbits, along with wild hyperbolic sets.