ABSTRACT Let be a dynamical system, where is a compact metric space and is a continuous map. Using the concepts of g-almost product property and uniform separation property introduced by Pfister and Sullivan in Pfister and Sullivan [On the topological entropy of saturated sets, Ergodic Theory Dyn. Syst. 27 (2007), pp. 929–956], we give a variational principle for certain non-compact with relation to the asymptotically additive topological pressure. We also study the set of points that are irregular for a collection finite or infinite of asymptotically additive sequences and we show that carried the full asymptotically additive topological pressure. These results are suitable for systems such as mixing shifts of finite type, β-shifts, repellers and uniformly hyperbolic diffeomorphisms.

中文翻译：

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渐近可加拓扑压力：不规则集非紧集和交集的变分原理

摘要 设一个动力系统，其中 是一个紧度量空间， 是一个连续映射。使用Pfister and Sullivan在Pfister and Sullivan [On the topological entropy of饱和集, Ergodic Theory Dyn. 系统。27 (2007), pp. 929–956]，我们给出了与渐近可加拓扑压力相关的某些非紧致的变分原理。我们还研究了一组有限或无限渐进加性序列的不规则点集，我们证明了它们承载了完整的渐进加性拓扑压力。这些结果适用于有限类型的混合位移、β-位移、排斥和均匀双曲微分同胚等系统。