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International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko
November 30, 2018 11:55–12:35, Moscow, Steklov Mathematical Institute (Gubkina, 8, 9th floor)
 


Ergodicity, mixing and KAM

Sergei Kuksin

Université Paris – 7
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Sergei Kuksin
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Abstract: To prove the ergodicity for Hamiltonian systems of big or infinite dimension is a notoriously complicated problem of high importance. But what we often have in physics are not Hamiltonian systems, but systems of the form <Hamiltonian system> + <small dissipation> + <small random forcing>, where the random forcing may be very degenerate (i.e. it affects only a few modes). For such systems an analogy of the ergodicity is called the mixing. In my talk I will remind the definition of the mixing and explain how the KAM-theory provides a powerful tool to prove the mixing for the systems above. The talk is based on a joint work with Armen Shirikyan and Vahagn Nersesyan [1]

Language: English

References
  1. Nersesyan, V.; Shirikyan, A.R.; Kuksin, S.B., Exponential mixing for a class of dissipative PDEs with bounded degenerate noise, arXiv: 1802.03250


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