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  • 天元講堂04(1.7,1.9) Nonhyperbolic measures and Lyapunov exponents of linear cocycles
  • 浏覽量:10 發布人: 發布時間:2019-12-31
  • 題目  Nonhyperbolic measures and Lyapunov exponents of linear cocycles: Part I
    報告人:Katrin Gelfert(Federal University of Rio de Janeiro (University of Brazil)
    時間  2020年1月7日 10:00-12:00
    地點   精正樓307
    摘要   In this talk I will discuss recent advances towards a thermodynamic formalism of partially hyperbolic dynamical systems. One particular focus will be on the multifractal analysis of the topological entropy spectrum of Lyapunov exponents. As a simple, but still very rich, model for partially hyperbolic dynamics, we will study step skew product systems with a shift dynamics in the base and circle diffeomorphisms as fiber maps. Important examples in this context are diffeomorphisms which arise from the projective action of SL(2,R) matrices on the circle. 



    題目  Nonhyperbolic measures and Lyapunov exponents of linear cocycles: Part II

    報告人:Katrin Gelfert(Federal University of Rio de Janeiro (University of Brazil)
    時間  2020年1月9日 10:00-12:00
    地點   精正樓307
    摘要  The most interesting case occurs when some matrix is hyperbolic and some elliptic (e.g. a rotation by some irrational angle).  The viewpoint of the so-called cocycle of matrix products as a partial hyperbolic dynamical system enables us to describe the spectrum of its Lyapunov exponents (the exponential growth rate of the norm of those matrix products). One essential ingredient in this study will be the description of the space of ergodic measures, where the presence of nonhyperbolic measures play an essential role.
    This is joint work with Lorenzo J. Diaz and Michal Rams.


    邀請人:楊大偉

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