A Variational Principle for the Pressure of Continuous Transformations

Introduction. Ruelle ([17]) has defined the concept of pressure for a continuous Zn action on a compact metric space and proved a variational principle when the action is expansive and satisfies the specification condition. We prove this variational principle, for the case of a Z + action, without these assumptions (Theorem 4.1). The method of proof extends that used by Dinaburg ([5]) and Goodman ([7]) to prove special cases of the result. Several definitions of pressure are given in Sec. 1 and properties of pressure are proved in Sec. 2. Part of the variational principle is proved in Sec. 3 and the proof is completed in Sec. 4. Some remarks on other results appear in Sec. 5.