Generic hyperbolic Ma\~n\'e sets have zero entropy

TL;DR

This paper proves that for generic hyperbolic Mañé sets in the $C^k$ topology, the topological entropy is zero, indicating a form of simplicity in their dynamical complexity.

Contribution

It establishes that generically, hyperbolic Mañé sets have zero entropy, a new result linking hyperbolicity and entropy in dynamical systems.

Findings

Hyperbolic Mañé sets have zero topological entropy in the $C^k$ topology.

The result applies to generic hyperbolic Mañé sets, indicating typical behavior.

Provides insight into the complexity of hyperbolic invariant sets.

Abstract

We prove that in the $C^k$ topology generic hyperbolic Ma\~n\'e sets have zero topological entropy.