Aubry–Mather Theory for Conformally Symplectic Systems

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.

URI:

https://hdl.handle.net/10651/70873

DOI:

10.1007/s00220-017-2900-3

Patrocinado por:

We would like to express our gratitude to Alessandra Celletti for her interest in this work and for many fruitful discussions. SM acknowledges the support of Marie Curie Initial Training Network Stardust, FP7-PEOPLE-2012-ITN, Grant Agreement 317185. AS has been partially supported by the PRIN- 2012-74FYK7 grant “Variational and perturbative aspects of nonlinear differential problem”.