Dynamics of globally minimizing orbits in contact Hamiltonian systems

TL;DR

This paper investigates the long-term behavior of globally minimizing orbits in contact Hamiltonian systems, showing their asymptotic limits are contained within semi-static orbits under certain conditions.

Contribution

It provides new insights into the asymptotic properties of globally minimizing orbits in contact Hamiltonian systems, linking their omega-limit sets to semi-static orbits.

Findings

Omega-limit set of globally minimizing orbits is contained in semi-static orbits

Under certain assumptions, asymptotic behavior is characterized

Results contribute to understanding long-term dynamics in contact Hamiltonian systems

Abstract

In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the $\omega$-limit set of globally minimizing orbits is contained in the set of semi-static orbits.