A VARIATIONAL PRINCIPLE FOR THE PRESSURE OF CONTINUOUS TRANSFORMATIONS.
A VARIATIONAL PRINCIPLE FOR THE PRESSURE OF CONTINUOUS TRANSFORMATIONS.
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DOI：
10.2307/2373682
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发表时间：
1975-01
影响因子：
1.7
通讯作者：
P. Walters
中科院分区：
文献类型：
--
作者：
P. Walters
引言。吕埃勒（[17]）针对紧致度量空间上的连续\(Z^n\)作用定义了压力的概念，并在作用是扩张的且满足特定条件时证明了一个变分原理。我们在\(Z^+\)作用的情形下，无需这些假设证明了这个变分原理（定理4.1）。证明方法扩展了迪纳伯格（[5]）和古德曼（[7]）用于证明该结果特殊情形的方法。第1节给出了压力的几种定义，第2节证明了压力的性质。变分原理的一部分在第3节得到证明，整个证明在第4节完成。第5节给出了关于其他结果的一些说明。
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.