Workshop on Chaos and Ergodicity of Realistic Hamiltonian Systems

December 11-14, 2007
Organizers: H. Broer (Groningen), P. Tupper (McGill)

In statistical physics the dynamical systems defined by the mechanics of large system of interacting particles is often assumed to be ergodic. Ergodicity for Hamiltonian systems means (roughly) that all points in phase space are equally likely to be visited by most trajectories of the system.  However, this appears to be contradicted by results in the theory of Hamiltonian systems that imply that ergodicity is not a generic property.  Much work has gone into contriving sufficient conditions for a Hamiltonian system to be ergodic.  Unfortunately, Hamiltonian systems that arise in applications almost never satisfy these conditions.  This workshop will investigate what is true of the ergodic properties of flows arising from these systems. Question we will address are:

  • Is mathematical ergodicity too strong a property for realistic systems?
  • What is the relation between chaos and ergodicity for Hamiltonian systems?
  • What about stronger properties, such as mixing, and CLT?
  • What are the limits imposed by KAM?
  • What is the relevance to molecular dynamics and fluid mechanics?
  • What are the prospects for the Arnold-Avez Conjecture: For rather general Hamiltonian systems show that areas of positive measure exist with positive Lyapunov exponent.