Abstract
In this paper, we study transitivity on the semigroup actions. Indeed, we introduce two criteria, “entropy minimality” and “nonuniformly expanding property”, to obtain transitivity.
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Alves, J.F., Vilarinho, H.: Strong stochastic stability for non-uniformly expanding maps. Ergod. Theory Dyn. Syst. 33, 647–692 (2013)
Barge, M., Martin, J.: Dense orbits on the interval. Michigan Math. J. 34, 3–11 (1987)
Bis, A.: Entropies of a semigroup of maps. Discrete Cont. Dyn. Syst. 11, 639–648 (2004)
Bis, A., Urbanski, M.: Some remarks on topological entropy of a semigroup of continuous maps. Cubo 8, 63–71 (2006)
Carvalho, M., Rodrigues, F., Varandas, P.: Semigroup actions of expanding maps. J. Stat. Phys. 166(1), 114–136 (2017)
Coven, E.M., Smital, J.: Entropy-minimality. Acta Math. Univ. Comen. 62, 117–121 (1993)
Eberlein, E.: On topological entropy of semigroups of commuting transformations. Asterisque 40, 17–62 (1976)
Gu, R.: The asymptotic average shadowing property and transivity. Nonlinear Anal. 67, 1680–1689 (2007)
Homburg, A.J., Nassiri, M.: Robust transitivity of iterated function systems with two generators. Ergod. Theory Dyn. Sys. 34, 1914–1929 (2014)
Koropecki, A., Nassiri, M.: Transitivity of generic semigroup of area preserving surface diffeomorphisms. Math. Z. 266, 707–718 (2010)
Kolyda, S., Snoha, L.: Some aspects of topological transitivity—a survay. Grazer Math. Ber. 334, 3–35 (1997)
Mohtashamipour, M., Zamani Bahabadi, A.: Accessibility on iterated function systems (preprint)
Mohtashamipour, M., Zamani Bahabadi, A.: Two-sided limit shadowing property on iterated function systems (preprint)
Rashid, A.A., Zamani Bahabadi, A.: Ergodicity of non-uniformly expanding transitive group (or semigroup) actions. J. Math. Phys. 57, 1–9 (2016)
Robinson, C.: Dynamical Systems, Stability, Symbolic Dynamics, and Chaos. Studies in Advanced Mathematics. CRC, Boca Raton (1999)
Rodrigues, F.B., Varandas, P.: Specification and thermodynamical properties of semigroup actions. J. Math. Phys. 57(5), 052704 (2016)
Sarizadeh, A.: Ergodicity of iterated function systems via minimality oh hyper spaces (2015). arxiv: 1510.08703v2 [math.DS].
Zamani Bahabadi, A.: Asymtotic average shadowing property on nonuniformly expanding maps. N. Y. J. Math. 20, 431–439 (2014)
Zamani Bahabadi, A.: Shadowing and average shadowing properties for iterated function systems. Georgian Math. J. 22(2), 179–184 (2015)
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Mohtashamipour, M., Zamani Bahabadi, A. Some Criteria for Transitivity of Semigroup Actions. Mediterr. J. Math. 15, 110 (2018). https://doi.org/10.1007/s00009-018-1159-z
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DOI: https://doi.org/10.1007/s00009-018-1159-z