The thermodynamic formalism for sub-additive potentials
Yongluo Cao - Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu, 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.
Received: November 2006; Revised: June 2007; Published: December 2007.
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