Qualitative Estimates of Topological Entropy for Non-Monotone Contact Lax-Oleinik Semiflow

TL;DR

This paper provides qualitative estimates of the topological entropy for the Lax-Oleinik semiflow associated with non-monotone contact Hamilton-Jacobi equations, highlighting its expansive nature.

Contribution

It offers the first qualitative bounds on the topological entropy for this class of semiflows, advancing understanding of their dynamical complexity.

Findings

Topological entropy bounds are established for the semiflow.

The semiflow exhibits expansive behavior.

Results contribute to the dynamical analysis of contact Hamilton-Jacobi equations.

Abstract

For the non-monotone Hamilton-Jacobi equations of contact type, the associated Lax-Oleinik semiflow $(T_t, C(M))$ is expansive. In this paper, we provide qualitative estimates for both the lower and upper bounds of the topological entropy of the semiflow.