集值映射下Packing熵的变分原理

V ariational principles of Packing topological entropies for set-valued maps

为了丰富动力系统中熵理论的研究,在度量空间中定义了半度量函数dn,并引入集值映射,在该条件下定义子集上Packing拓扑熵,得到子集上Parking拓扑熵的变分原理为h^(P)_(top)(f,K)=sup{h_(μ)(f):μ∈M(X),μ(K)=1},其中h^(P)_(top)(f,K)是集合K的Packing拓扑熵.

In order to enrich the study of entropy theory in dynamical systems,the semi metric function d.was defined in the metric space.The set-valued mapping was introduced.Under this condition,the packing topological entropy on the subset was defined,and the variational principle of the parking topological entropy on the subset was obtained,i.e.h^(P)_(top)(f,K)=sup{h_(μ)(f):μ∈M(X),μ(K)=1},where h^(P)_(top)(f,K)was packing topological entropy of K.