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.


Math 231 "Calculus of Several Variables", Syllabus.



  • 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