非紧集上的变分原理

On the variational principle for the topological entropy of certain non-compact set

对紧度量空间(X,d),T∶X→X是连续映射,μ是遍历不变测度,我们考虑集合K,它是使得-logμ(Bn(x,ε))n关于n以及ε的极限等于测度熵hμ(T)的那些X中的点所构成的集合.我们证明了变分原理:测度熵hμ(T)等于测度为1的集合的拓扑熵的下确界.事实上我们证到了测度熵hμ(T)就等于集合K的拓扑熵.

For a continuous transformation T of a compact space (X,d),μ is ergodic,we consider the set K,it consists of all points x∈X that the limits of -logμ(B_n(x,ε))n with respect to n and ε is equal to the measure theoretic entropy h_μ(T).We prove h_μ(T)=h_(top)(T,K).