On the topological pressure of the saturated set with non-uniform structure

Cao Zhao, Ercai Chen

DOI: http://dx.doi.org/10.12775/TMNA.2017.048

Abstract


We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including $\beta$-shifts, $S$-gap shifts and their subshift factors.

Keywords


Non-uniform structure; topology pressure; saturated set; irregular set

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References


L. Barreira and B. Saussol, Variational principles and mixed multifractal spectra, Trans. Amer. Math. Soc. 353 (2001), 3919–3944.

L. Barreira, B. Saussol and J. Schmeling, Higher-dimensional multifractal analysis, J. Math. Pures Appl. 81 (2002), 67–91.

L. Barreira and J. Schmeling, Sets of “non-typical” points have full topological entropy and full Hausdorff dimension, Israel J. Math. 116 (2000), 29–70.

E. Chen, T. Kupper and L. Shu, Topological entropy for divergence points, Ergodic Theory Dynam. Systems 25 (2005), 1173–1208.

V. Climenhaga, D. Thompson and K. Yamamoto, Large deviations for systems with non-uniform structure, Trans. Amer. Math. Soc. 369 (2017), 4167–4192.

G. Dimitrios and Y. Peres, Invariant measures of full dimension for some expanding maps, Ergodic Theory Dynam. Systems 17 (1997), 147–167.

L. Olsen, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. IV Divergence points and packing dimension, Bull. Sci. Math. 132 (2008), 650–678.

L. Olsen and S. Winter, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II Non-linearity, divergence points and Banach space valued spectra, Bull. Sci. Math. 131 (2007), 518–558.

Y. Pei and E. Chen, On the variational principle for the topological pressure for certain non-compact sets, Sci. China. Math. 53 (2010), 1117–1128.

Y. Pesin, Dimension Theory in Dynamical Systems, Contemporary Views and Applications, University of Chicago Press (1997).

C.-E. Pfister and W. Sullivan, On the topological entropy of saturated sets, Ergodic Theory Dynam. Systems 27 (2007), 929–956.

F. Takens and E. Verbitskiy, On the variational principle for the topological entropy of certain non-compact sets, Ergodic Theory Dynam. Systems 23 (2003), 317–348.

D. Thompson, A variational principle for topological pressure for certain non-compact sets, J. London Math. Soc. 80 (2009), 585–602.

D. Thompson, Irregular sets, the β-transformation and the almost specification property, Trans. Amer. Math. Soc. Ser. 364 (2012), 5395–5414.

P. Walter, An Introduction to Ergodic Theory, Springer, Berlin, 1982.

X. Zhou and E. Chen, Multifractal analysis for the historic set in topological dynamical systems, Nonlinearity 26 (2013), 1975–1997.


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