Aubry-Mather Theory for Conformally Symplectic Systems

Abstract

In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.

32 pages

References in corpus (3)

• Convergence of the solutions of the discounted equation
• Convergence of the solutions of the discounted equation: the discrete case
• Young measures, superposition and transport

Cited by in corpus (9)

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• Conformal Symplectic and Relativistic Optimization
• Convergence of viscosity solutions of generalized contact Hamilton-Jacobi equations
• Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
• Global dynamics of contact Hamiltonian systems (I): monotone systems
• Existence of whiskered KAM tori of conformally symplectic systems
• Birkhoff attractors of dissipative billiards
• Homogeneous bi-Hamiltonian structures and integrable contact systems
• Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps