Finiteness of attractors and repellers on sectional hyperbolic sets

TL;DR

This paper establishes an upper bound on the number of attractors and repellers that can emerge from small perturbations of sectional hyperbolic sets, extending previous results in higher-dimensional flows.

Contribution

It provides a new upper bound for the number of attractors and repellers in sectional hyperbolic sets under perturbations, advancing understanding of their stability and structure.

Findings

Upper bound for attractors and repellers established

Extension of previous results to higher dimensions

Insights into stability of sectional hyperbolic sets

Abstract

We obtain an upper bound for the number of attractors and repellers that can appear from small perturbations of a sectional hyperbolic set. This extends results from [Sectional-Anosov flows in higher dimensions] and [The explosion of singular-hyperbolic attractors].