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

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.