Persistence of normally expanded submanifolds with boundary or corners

TL;DR

The paper proves that normally expanded invariant submanifolds with boundary or corners are persistent as stratifications in class C^s, with an example showing non-persistence in certain cases.

Contribution

It establishes persistence of normally expanded submanifolds with boundary or corners as stratifications, extending previous results to include boundaries and corners.

Findings

Persistence of normally expanded submanifolds with boundary or corners as stratifications.

Existence of a normally expanded submanifold with boundary that is not persistent as a differentiable submanifold.

Results are shown in class C^s, for s ≥ 1.

Abstract

We show that invariant submanifolds with boundary, and more generally with corners which are normally expanded by an endomorphism are persistent as $a$-regular stratifications. This result will be shown in class $C^s$, for $s\ge 1$. We present also a simple example of a submanifold with boundary which is normally expanded but non-persistent as a differentiable submanifold.