Density of Axiom A for area contracting surface embeddings

TL;DR

This paper proves that Axiom A systems are generically prevalent among area-contracting surface embeddings, confirming the area contracting version of Smale's conjecture.

Contribution

It establishes that Axiom A is open and dense in the space of $C^1$ area contracting surface embeddings, settling a key conjecture.

Findings

Axiom A is open in the space of $C^1$ area contracting embeddings.

Axiom A is dense in this space, showing genericity.

The result confirms the area contracting version of Smale's conjecture.

Abstract

We prove that Axiom A is open and dense in the space of $C^1$ area contracting orientation-preserving embeddings on compact orientable surfaces with boundary. This settles the area contracting version of the {\em Smale's conjecture} \cite{s}.