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.
Acknowledgments
The author is grateful to P. Varandas and V. Ramos for providing a preliminary version of this paper and making important suggestions that helped improve the presentation of the text. The author is also grateful to anonymous referees for giving us a simpler proof for the Theorem A and suggestions that helped to improve the text.
Disclosure statement
No potential conflict of interest was reported by the author.