Variational principle for weighted topological pressure

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• 作者：De-Jun Feng^a ; ^{djfeng@math.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author} ; Wen Huang^b ; ^c ; ^{wenh@mail.ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37D35 ; 37C45 ; 37B40
• 刊名：Journal de mathematiques pures et appliquees
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：106
• 期：3
• 页码：411-452
• 全文大小：714 K

文摘

Let (X,T)$(X,T)$ and (Y,S)$(Y,S)$ be two topological dynamical systems, and π:X→Y$\pi :X\to Y$ a factor map. Let a=(a₁,a₂)∈R²$\mathbf{a}=(a_1,a_2)\in {\mathbb{R}}^2$ with a₁>0$a_1>0$ and a₂≥0$a_2\ge 0$, and 34b" title="Click to view the MathML source">f∈C(X)$f\in C(X)$. We define the a-weighted topological pressure of f  , denoted by P^a(X,f)$P^{\mathbf{a}}(X,f)$, as an extension of the classical topological pressure. In this approach, we use the a-weighted Bowen balls to substitute the Bowen balls in the classical definition. We prove the following variational principle: where the supremum is taken over the T-invariant measures on X  . It not only generalizes the variational principle of classical topological pressure, but also provides a topological extension of dimension theory of invariant sets and measures on the torus T²${\mathbb{T}}^2$ under affine diagonal endomorphisms. A higher dimensional version of the result is also established.