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Jung-Chao Ban

2008-03-07
10:00:00 - 11:30:00

Thermodynamic Formalism：An Introduction

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this lecture, we will focus on the key of the thermodynamic formalism, the topological pressure, and discuss its Gibbs property, equilibrium measures, the relations to the information theory, classical dimension theory and Poincare recurrence. Finally, will also give a brief survey of the topic for multifractal analysis, which is the popular topic in dynamical systems of nowadays. [1] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics, Springer‐Verlag, Berlin‐New York. [2] Ya. Pesin, Dimension theory in dynamical systems: contemporary views and applications, Chicago Univ. Press, 1997. [3]D.Ruelle, Thermodynamic Formalism. Addison‐Wesley, 1978. [4] P. Walters, A Variational Principle for the Pressure of Continuous Transformations. Amer. J. Math. 97 (1971), 937‐971.