I am Distinguished Professor at the Department of Mathematics of The Pennsylvania State University and a member of The Center for Dynamics and Geometry at Penn State


I am Fellow of American Mathematical Society



Dynamical Systems, Ergodic Theory, Riemannian Geometry, Dimension Theory, Mathematical and Statistical Physics


I am an Editor of Ergodic Theory and Dynamical Systems

I am an Associate Editor of Chaos, Solitons & Fractals


Michael Brin Prize in Dynamical Systems, Winners of Michael Brin Prize : Giovanni Forni -- 2008, Dmitry Dolgopyat -- 2009, Artur Avila -- 2011, Omri Sarig --2013


Math 501 Real Analisys A, Solutions of Midterm problems and HW 7, 8, 9, 10, 11, 12, Final topics and problem's solutions



  • General Theory of Smooth Dynamical Systems,
    Encyclopedia of Mathematical Sciences 100, in the book: Dynamical systems. II. Ergodic theory with applications to dynamical systems and statistical mechanics, Edited by Ya. Sinai, second edition, Springer-Verlag, New York--Berlin, 1999
  • The Essential Coexistence Phenomenon in Dynamics (with J. Chen and H. Hu),
    special issue ``Statistical Properties of Dynamical Systems'', Dynamical Systems, an International Journal (Ed. M. Nicol, P. Ashwin), v. 28, 2013; this is an Author's Original Manuscript of the article published in the journal [copyright Taylor & Francis], the journal is available on http://www.tandfonline.com

While mathematics is about abstract thinking, art is about abstract vision. See