Properties of compact center-stable submanifolds

TL;DR

This paper investigates the characteristics and limitations of compact center-stable submanifolds within partially hyperbolic systems, establishing finiteness results and conditions for their existence and intersections.

Contribution

It provides new theoretical results on the finiteness and existence conditions of compact center-stable submanifolds in partially hyperbolic systems.

Findings

A partially hyperbolic system can have only finitely many such submanifolds.

Sufficient conditions for the existence of these submanifolds are identified.

The paper explores the potential intersections among these submanifolds.

Abstract

We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect each other.