On isolated periodic points of diffeomorphisms with expanding attractors of codimension 1

TL;DR

This paper investigates the minimum number of isolated periodic points in a specific class of 3-dimensional dynamical systems with certain stable attractors, providing estimates based on attractor structure.

Contribution

It introduces a method to estimate the minimal number of isolated periodic points for $ ext{Ω}$-stable 3-diffeomorphisms with codimension 1 expanding attractors.

Findings

Provides lower bounds for isolated periodic points

Analyzes the role of attractor structure in periodic point count

Addresses both orientable and non-orientable attractors

Abstract

In the paper we consider an $\Omega$-stable 3-diffeomorphism, chain recurrent set of which consists of isolated periodic points and expanding attractors of codimension 1, orientable or not. We estimate a minimum number of isolated periodic points using information about the structure of the attractors.