On the dynamics of contact Hamiltonian systems: I. Monotone 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 dynamical and topological properties. This is based on an analysis from the viewpoint of gradient-like systems.