Document Zbl 1499.37017

Saturatedness of dynamical systems under the almost specification property. (English) Zbl 1499.37017

J. Dyn. Syst. Geom. Theor. 14, No. 1, 1-15 (2016).

MSC:

37B05	Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37C45	Dimension theory of smooth dynamical systems

Keywords:

almost specification property; \(V\)-statistics

Cite Review PDF

Full Text: DOI

References:

[1]	Bergelson, V., Weakly mixing PET, Ergod. Th. and Dynam. Sys., 7, 337-349 (1987) · Zbl 0645.28012 · doi:10.1017/S0143385700004090
[2]	Bourgain, J., Double recurrence and almost sure convergence, J. Reine Angew Math, 404, 140-161 (1990) · Zbl 0685.28008
[3]	Bowen, R., Topological entropy for non-compact sets, Trans. Amer. Math. Soc.,, 184, 125-136 (1973) · Zbl 0274.54030 · doi:10.1090/S0002-9947-1973-0338317-X
[4]	Buszzi, J., Specification on the interval, Trans. Amer. Math. Soc., 349, 2737-2754 (1997) · Zbl 0870.58017 · doi:10.1090/S0002-9947-97-01873-4
[5]	Fan, A. H.; Schmeling, J.; Wu, J., The multifractal spectrta of V −statistics (2012)
[6]	Fan, A.; Liao, I. M.; Peyrière, J., Generic points in systems of specification and Banach valued Birkhoff averages, Disc. Cont. Dynam. Sys.,, 21, 1103-1128 (2008) · Zbl 1153.37318 · doi:10.3934/dcds.2008.21.1103
[7]	Furstenberg, H., Ergodic behavior of diagonal measures and a theorem of Szmeŕedi on arith- metic progressions, J. dÁnalyse Math, 31, 204-256 (1977) · Zbl 0347.28016 · doi:10.1007/BF02813304
[8]	Meson, A.; Vericat, F., On The topological entropy of the irregular part of V-statitistics multifractal spectra, J. Dynam. Sys. and Geom. Theories,, 11, 1-12 (2013) · Zbl 1306.37028 · doi:10.1080/1726037X.2013.810440
[9]	Meson, A.; Vericat, F., On the irregular part of V −statistics multifractal spectra for systems with non-uniform specification, J. Dynam. Sys. and Geom. Theories,, 13, 1-26 (2015) · Zbl 1499.37058 · doi:10.1080/1726037X.2015.1027108
[10]	Pfister, C. E.; Sullivan, W. G., On the topological entropy of saturated sets, Ergod. Th. and Dynam. Sys., 27, 1-29 (2007) · Zbl 1130.37329 · doi:10.1017/S0143385706000824
[11]	Schmeling, J., Symbolic dynamics for beta-shift and self-normal numbers, Ergod. Th. and Dynam. Sys., 17, 675-694 (1997) · Zbl 0908.58017 · doi:10.1017/S0143385797079182
[12]	Takens, F.; Verbitski, E., On the variational principle for the topological entropy of certain non-compact sets, Ergod. Th. and Dynam. Sys.,, 23, 317-348 (2003) · Zbl 1042.37020 · doi:10.1017/S0143385702000913
[13]	Thompson, D., The irregular set for maps with the specification property has full topological pressure, Dynam Sys: An InternationalJournal, 25, 1, 25-51 (2010) · Zbl 1186.37034 · doi:10.1080/14689360903156237
[14]	Varandas, P., Non-uniform specification and large deviations for weaks Gibbs measures, J. Stat. Phys., 146, 330-358 (2012) · Zbl 1245.82038 · doi:10.1007/s10955-011-0392-7
[15]	Young, L. S., Large deviations in dynamical systems, Trans. Amer. Math. Soc.,, 318, 525-543 (1990) · Zbl 0721.58030

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.