Dynamics of slow-fast Hamiltonian systems

• 主讲人：Sergey Bolotin (Steklov Mathematical Institute of RAS)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2024-04-26 17:00 - 2024-04-26 18:00
• 地点： online

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Abstract: Slow-fast Hamiltonian systems appear in many applications, in particular in the problem of Arnold's diffusion. When the slow variables are fixed we obtain the frozen system. If the frozen system has one degree of freedom and the level curves of the frozen Hamiltonian are closed, there is an adiabatic invariant which governs evolution of the slow variables. Near a separatrix of the frozen system the adiabatic invariant is destroyed. A.Neishtadt proved that at a crossing of the separatrix the adiabatic invariant has "random" jumps and the slow variables evolve in a quasi-random way. In this talk we discuss partial extension of Neishtadt's results to multidimensional slow-fast systems. The slow variables shadow trajectories of an effective Hamiltonian system which depends on a "random" integer parameter.

 

Bio: Sergey Bolotin is a specialist in Hamiltonian systems, variational methods and celestial mechanics. He is a corresponding member of the Russian Academy of Sciences. He was an invited speaker at ICM 1994 in Zürich at the section "Ordinary Differential Equations". He is a principal scientific researcher at the Steklov Mathematical Institute of RAS and also a head of the department of mechanics. He is a professor at Moscow State University. He was a professor at University of Wisconsin-Madison, USA, and is now professor emeritus there.