Existence of periodic orbits for singular-hyperbolic Lyapunov stable sets

TL;DR

This paper extends the known existence of periodic orbits from singular-hyperbolic attracting sets to more general singular-hyperbolic Lyapunov stable sets, broadening the understanding of their dynamical structure.

Contribution

It generalizes previous results by proving the existence of periodic orbits in singular-hyperbolic Lyapunov stable sets, not just attracting sets.

Findings

Periodic orbits exist in singular-hyperbolic Lyapunov stable sets

Extension of previous results to broader class of sets

Enhances understanding of the structure of singular-hyperbolic systems

Abstract

Bautista and Morales proved the existence of periodic orbits in singular-hyperbolic attracting sets(*). In this paper, we extend their result to singular-hyperbolic Lyapunov stable sets. ((*)"Existence of periodic orbits for singular-hyperbolic sets", Moscow Mathematical Journal, 6 (2006), 265-297)