Attractors with Non-Invariant Interior and Pinheiro's Theorem A

TL;DR

This paper investigates the properties of attractor interiors in smooth maps, providing a straightforward proof of Pinheiro's Theorem A and exploring conditions under which attractors have non-invariant interiors.

Contribution

It offers a new, simplified proof of Pinheiro's Theorem A and extends understanding of attractor interior properties in smooth maps beyond diffeomorphisms.

Findings

Proof of Pinheiro's Theorem A

Conditions for non-invariant attractor interiors

Insights into attractor properties in smooth maps

Abstract

This is a provisional version of an article, intended to be devoted to properties of attractor's intertior for smooth maps (not diffeomorphisms). We were originally motivated for this research by Pinhero's Theorem A from his recent preprint, and in Section 3 we give a simple and straightforward proof of this result.