连续自映射拓扑压的两个注记

令T:X→ X是紧度量空间(X,d)上的连续映射.该文给出了T的拓扑压和T在非游荡集上的限制的拓扑压相等的不依赖于变分原理的一个直接证明.同时,还讨论了半共轭的两个系统的拓扑压之间的关系,证明了拓扑压在一致有限对一条件下是半共轭不变量.

Two Notes on the Topological Pressure of the Continuous Self-mappings

Let T:X→X be a continuous mapping on a compact metric space (X,d). In this paper, the authors give a direct proof of the equality of the pressure of T and that of T restricted to its non-wandering set, P(T,f)=(T|_\Omega,f|_\Omega),f\in C(X,R,without applying the variational principle. The authors also discuss the relation of the pressures of two systems which are semiconjugate, and show that the pressure is invariant under the uniformly finite-to-one semi-conjugacy.