JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 109-113.doi: 10.6040/j.issn.1671-9352.0.2023.380

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Resilience of dynamical systems for the integer groups Z-partial actions

CHENG Dandan, WANG Guotao   

  1. School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, Shanxi, China
  • Published:2024-12-12

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Abstract: Dynamical systems for integer groups Z-partial action, the notions of various partially recurrent points are introduced. Simultaneously, the relationship and properties of various partially recurrent points are studied. Finally, we investigate the relationship of various partially recurrent points of two semi-equivalent topological partial actions.

Key words: integer groups Z-partial action, partially periodic point, partially ω limit point set, partially topological transitive, partially non-wandering point

CLC Number: 

  • O192
[1] BARAVIERA A, GONCALVES D, ROYER D, et al. Topological entropy for partial actions of the group Z[EB/OL].(2015-09-20)[2023-04-09]. http://arxiv.org/abs/1509.0614v4.
[2] DOKUCHAEV M, EXEL R. Partial actions and subshifts[J]. Journal of Functional Analysis, 2017, 272(12):5038-5106.
[3] EXEL R. Circle Actions on C*-algebras, partial automorphisms and generalized pimsner voiculescu exect sequences[J]. Journal of Functional Analysis, 1994, 122(2):361-401.
[4] EXEL R, LACA M, QUIGG J. Partial dynamical systems and C*-algebras generated by partial isometries[J]. Journal of Operator Theory, 2002, 47(1):169-186.
[5] EXEL R. Partial dynamical systems, fell bundles and Applications[M]. Providence: American Mathematical Society, 2017.
[6] BARREIRA L. Ergodic theory, hyperbolic dynamics and dimension theory[M]. Heidelberg: Springer, 2012.
[7] CHENG D, LI Z. Mean dimensions for partial actions[J]. Journal of Difference Equations and Applications, 2020, 26(4): 561-573.
[8] CARVALHO M, RODRIGUES F B, VARANDAS P. Semigroup actions of expanding maps [J]. Journal of Statistical Physics, 2017, 166(1):114-136.
[9] DOKUCHAEV M. Partial actions: a survey[M] //DOKUCHAEV M. Groups, Algebras and Applications. Providence: American Mathematical Society, 2011:173-184.
[10] DOKUCHAEV M. Recent development around partial actions [J].São Paulo Journal of Mathematical Sciences, 2019, 13(1):195-247.
[11] LI T, YORKE Y. Period three implies chaos [J]. American Mathematical Monthly, 1975, 82:985-992.
[12] GU R, SUN T, ZHENG T. Non-wandering set of a continuous graph map [J]. Applied Mathematics, 2003, 18:477-481.
[13] HUANG W, YE X. Non-wandering sets of the powers of maps of a tree [J]. Science in China(Series A), 2001, 44:31-39.
[14] MAKHROVA E N, VANIUKOVA K S. On the set of non-wandering points of monotone maps on local dendrites [J]. Journal of Physics, 2016, 692:012012.
[15] MAI J, SHAO S. Spaces of ω-limit sets of graph maps[J]. Fundamenta Mathematicae, 2007, 196:91-100.
[16] MAI J, SUN T. The ω-limit set of a graph map[J]. Topology and Its Applications, 2007, 154:2306-2311.
[17] AKIN E C, JEFFREY D. Conceptions of topological transitivity[J]. Topology and Its Applications, 2012, 159(12):2815-2830.
[18] SALMAN M, DAS R. Multi-transitivity in non-autonomous discrete systems[J].Topology and Its Applications, 2020, 278:107237.
[19] YAN K, LIU Q, ZENG F. Classification of transitive group actions[J]. Discrete and Continuous Dynamical Systems. 2021, 41(12):5579-5607.
[20] 叶向东,黄文,邵松. 拓扑动力系统概论[M]. 北京:科学出版社, 2008:3-25. YE Xiandong, HUANG Wen, SHAO Song. Introduction to topological dynamical systems[M]. Beijing: Science Press, 2008:3-25.
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