Dynamics of physical systems , normal forms and Markov chains

Abstract : This thesis deals with the questions of asymptotic behavior of dynamical systems and consists of six independent chapters. In the first part of this thesis we consider three particular dynamical systems. The first two chapters deal with the models of two physical systems: in the first chapter, we study the geometric structure and limit behavior of Arnold tongues of the equation modeling a Josephson contact; in the second chapter, we are interested in the Lagrange problem of establishing the asymptotic angular velocity of the swiveling arm on the surface. The third chapter deals with planar geometry of an elliptic billiard.The forth and fifth chapters are devoted to general methods of studying the asymptotic behavior of dynamical systems. In the forth chapter we prove the convergence of markovian spherical averages for free group actions on a probablility space. In the fifth chapter we provide a normal form for skew-product diffeomorphisms that can be useful in the study of strange attractors of dynamical systems.
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Olga Romaskevich. Dynamics of physical systems , normal forms and Markov chains. Dynamical Systems [math.DS]. Université de Lyon, 2016. English. ⟨NNT : 2016LYSEN043⟩. ⟨tel-01417969v2⟩

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