A variational principle for topological pressure for certain non‐compact sets
A variational principle for topological pressure for certain non‐compact sets
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DOI：
10.1112/jlms/jdp041
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发表时间：
2008-09
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通讯作者：
D. Thompson
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文献类型：
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作者：
D. Thompson
设（X, d）是紧度量空间，设f:X∈X是一个具有规定性的连续映射，设φ: X∈一个连续函数。对于形式为{x∈x:limn→∞1n∑i−0n−1φ(fi(x))=α}的非紧集，我们证明了拓扑压力的变分原理（在Pesin和Pitskel意义上）。作为应用，我们证明了具有规范的连续映射上悬浮流的熵谱的多重分形分析结果和某些非均匀展开区间映射的维谱。
Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let φ: X ↦ ℝ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non‐compact sets of the form {x∈X:limn→∞1n∑i−0n−1φ(fi(x))=α} Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non‐uniformly expanding interval maps.