Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

The thermodynamic formalism for sub-additive potentials

Pages: 639 - 657, Volume 20, Issue 3, March 2008      doi:10.3934/dcds.2008.20.639

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Yongluo Cao - Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu, China (email)
De-Jun Feng - Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China (email)
Wen Huang - Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China (email)

Abstract: The topological pressure is defined for sub-additive potentials via separated sets and open covers in general compact dynamical systems. A variational principle for the topological pressure is set up without any additional assumptions. The relations between different approaches in defining the topological pressure are discussed. The result will have some potential applications in the multifractal analysis of iterated function systems with overlaps, the distribution of Lyapunov exponents and the dimension theory in dynamical systems.

Keywords:  Thermodynamical formalism, variational principle, topological pressure, Lyapunov exponents, entropy, products of matrices.
Mathematics Subject Classification:  Primary: 37D35; Secondary: 34D20.

Received: November 2006;      Revised: June 2007;      Available Online: December 2007.