Abstract:

The variational principle of topological pressure for sub-additive potentials was proved by Cao etal. This generalized variational principle plays an important role in the theory of dimension and equilibrium state for some expansive dynamical systems such as, for example, self-affine fractals and non-conformal repellers. The main purpose of this paper is to give another proof for the variational principle in the sub-additive case when the entropy map is upper semi-continuous.

Key words: Topological Pressure, Sub-additive Potential, Variational Principle