On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits

2025/01/02 by Jin Liang, Jun Yan, Jin, Liang +3
Physics and Astronomy · Engineering · Mathematics · #Quantum chaos and dynamical systems #Control and Stability of Dynamical Systems #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2501.01279

Abstract

This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \citeJY, but without monotonicity assumption. Due to the complexity of general cases, we focus on the behavior of action minimizing orbits. We pick out certain action minimizing invariant sets \\widetildeN_u\ in the phase space naturally stratified by solutions u to the corresponding Hamilton-Jacobi equation. Using an extension of characteristic method, we establish the existence of semi-infinite orbits that is asymptotic to some \widetildeN_u and heteroclinic orbits between \widetildeN_u and \widetildeN_v for two different solutions u and v.

Related

• Dynamics of globally minimizing orbits in contact Hamiltonian systems
• Contact Hamiltonian systems with nonholonomic constraints
• Contact topology and non-equilibrium thermodynamics
• The Hamilton--Jacobi theory for contact Hamiltonian systems
• Hyperbolic Orbits for a Class of Singular Hamiltonian Systems