One-Dimensional Dynamics and High-Dimensional Network Systems

Adiabatic invariant actions of partially integrable systems

Not scheduled

25m

Aula Dini (Palazzo del Castelletto)

Short Talk

Speaker

Amir Khodaeian Karim (Imperial college)

Description

We introduce action variables for partially integrable systems. We prove that for slow-fast partially integrable Hamiltonian systems, when the restriction of the Hamiltonian to the common level of the integrals is ergodic, a slow change of parameters creates geometrically defined adiabatic invariants that are integrals of the averaged system. This is in contrast to the absence of ergodcity. This work raises questions that stand in the crossroads of Ergodic Theory, Symplectic Topology, and Thermodynamics.
This is a joint work with Konstantinos Kourliouros and Dmitry Turaev.