Global dynamics of contact Hamiltonian systems (I): monotone systems

TL;DR

This paper explores the global behavior of monotone contact Hamiltonian systems, focusing on the structure and properties of their maximal attractors and repellers through a gradient-like systems perspective.

Contribution

It provides a detailed analysis of the phase flow dynamics and topological features of maximal attractors in monotone contact Hamiltonian systems.

Findings

Identification of the maximal attractor and repeller structures

Topological characterization of invariant sets

Insights into gradient-like behavior of the systems

Abstract

This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact invariant sets, and investigating its topological and dynamical properties. This is based on an analysis from the viewpoint of gradient-like systems.