The asymptotically additive topological pressure: variational principle for non-compact and intersection of irregular sets. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Ferreira, G.
• Is Part Of: Dynamical systems. Volume 34:Issue 3(2019)
• Page Start: 484
• Page End: 503
• Publication Date: 2019-07-03
• Subjects: Asymptotically additive topological pressure -- variational principle -- sequentially saturated -- specification property -- β-shifts -- hyperbolic systems -- nonconformal repellers -- cocycles under shift of the finite type; 37C50 -- 37C45 -- 37B10 -- 37D20; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1567689
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: Let ( X, d, f ) be a dynamical system, where ( X, d ) is a compact metric space and f : X → X 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.