280 research outputs found
Topological pressures for -stable and stable sets
Topological pressures of the preimages of -stable sets and some
certain closed subsets of stable sets in positive entropy systems are
investigated. It is showed that the topological pressure of any topological
system can be calculated in terms of the topological pressure of the preimages
of -stable sets. For the constructed closed subset of the stable set
or the unstable set of any point in a measure-theoretic `rather big' set of a
topological system with positive entropy, especially for the weakly mixing
subset contained in the closure of stable set and unstable set, it is proved
that topological pressures of these subsets can be no less than the
measure-theoretic pressure
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