# American Institute of Mathematical Sciences

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2008, 20(3): 639-657. doi: 10.3934/dcds.2008.20.639

## The thermodynamic formalism for sub-additive potentials

 1 Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu 2 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China 3 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026

Received  November 2006 Revised  June 2007 Published  December 2007

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.
Citation: Yongluo Cao, De-Jun Feng, Wen Huang. The thermodynamic formalism for sub-additive potentials. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 639-657. doi: 10.3934/dcds.2008.20.639
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