摘要本文对自由半群作用的动力系统引入了估计熵和Δ-弱混合集的概念,得到一些性质.通过引入Δ-熊混沌集,给出了Δ-弱混合集的一个等价刻画. | | 服务 | | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | 加入引用管理器 | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | E-mail Alert | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | RSS | 收稿日期: 2019-01-02 | | 基金资助:国家自然科学基金资助项目(11771459,11701584);广东外语外贸大学青年项目(18QN30)
| 作者简介: 钟兴富,E-mail:xfzhong@gdufs.edu.cn |
[1] Adler R. L., Konheim A. G., McAndrew M. H, Topological entropy, Transactions of the American Mathematical Society, 1965, 114(2):309-319. [2] Akin E., Lectures on Cantor and Mycielski sets for dynamical systems, Chapel Hill Ergodic Theory Workshops, 2004:21-79. [3] Bi? A., Entropies of a semigroup of maps, Discrete and Continuous Dynamical Systems, 2004, 11(2-3):639-648. [4] Blanchard F., Huang W., Entropy sets, weakly mixing sets and entropy capacity, Discrete & Continuous Dynamical Systems-Series A, 2012, 20(2):275-311. [5] Bowen R., Entropy for group endomorphisms and homogeneous spaces, Transactions of the American Mathematical Society, 1971, 153:401-401. [6] Bowen R., Topological entropy for noncompact sets, Transactions of the American Mathematical Society, 1973, 184:125-136. [7] Bufetov A., Topological entropy of free semigroup actions and skew-product transformations, Journal of Dynamical and Control Systems, 1999, 5(1):137-143. [8] Carrasco-Olivera D., Alvan R. M., Rojas C. A. M., Topological entropy for set-valued maps, Discrete & Continuous Dynamical Systems-Series B, 2015, 20(10):3461-3474. [9] Carvalho M., Rodrigues F. B., Varandas P., Quantitative recurrence for free semigroup actions, Nonlinearity, 2018, 31(3):864. [10] Chen Z., Li J., Lü J., Point transitivity, Δ-transitivity and multi-minimality, Ergodic Theory and Dynamical Systems, 2015, 35(5):1423-1442. [11] Colonius F., Kawan C., Nair G., A note on topological feedback entropy and invariance entropy, Systems & Control Letters, 2013, 62(5):377-381. [12] Colonius F., Kawan C., Invariance entropy for control systems, SIAM Journal on Control and Optimization, 2009, 48(3):1701-1721. [13] Dinaburg E. I, A correlation between topological entropy and metric entropy, Dokl. Akad. Nauk Sssr, 1970, 190:19-22. [14] Huang W., Li J., Ye X., et al., Positive topological entropy and Δ-weakly mixing sets, Advances in Mathematics, 2017, 306:653-683. [15] Huang Y., Zhong X., Carathéodory-Pesin structures associated with control systems, Systems & Control Letters, 2018, 112:36-41. [16] Huang Y., Zhong X., Topological entropy of switched systems, Journal of the Korean Mathematial Society, 2018, 55(5):1157-1175. [17] Huang Y., Zhong X., Weak Mixing of Switched Systems, Science China Mathematics, 2018, accepted. [18] Hui H., Ma D., Some remarks on measure-theoretic entropy for a free semigroup action, Taiwanese Journal of Mathematics, 2017, 21(2):429-440. [19] Hui H., Ma D., Some dynamical properties for free semigroup actions, Stochastics and Dynamics, 2018, 18(4):1850032(20pages). [20] Kawan C., Exponential state estimation, entropy and Lyapunov exponents, Systems & Control Letters, 2018, 113:78-85. [21] Kelly J., Tennant T., Topological entropy on set-valued functions, arXiv preprint arXiv:1509.08413, 2015. [22] Kurka P., Topological and Symbolic Dynamics, Société Mathématique de France, Paris, 2003. [23] Liberzon D., Mitra S., Entropy and minimal data rates for state estimation and model detection, In:Proceedings of the 19th International Conference on Hybrid Systems:Computation and Control, ACM, 2016, 247-256. [24] Lin X., Ma D., Wang Y., On the measure-theoretic entropy and topological pressure of free semigroup actions, Ergodic Theory & Dynamical Systems, 2018, 38:686-716. [25] Ma D., Wu M., Topological pressure and topological entropy of a semigroup of maps, Discrete Contin. Dyn. Syst., 2011, 31(2):545-557. [26] Matveev A., Pogromsky A., Observation of nonlinear systems via finite capacity channels:Constructive data rate limits, Automatica, 2016, 70:217-229. [27] Moothathu T. S., Diagonal points having dense orbit, Proceedings of Colloquium Mathematicum Instytut Matematyczny Polskiej Akademii Nauk, 2010, 120(1):127-138. [28] Nadler S. B., Hyperspaces of Sets, A Text with Research Questions, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49. Marcel Dekker, Inc., New York, Basel, 1978. [29] Nair G. N., Evans R. J., Mareels I. M. Y., et al., Topological feedback entropy and Nonlinear stabilization, IEEE Transactions on Automatic Control, 2004, 49(9):1585-1597. [30] Oprocha P., Coherent lists and chaotic sets, Discrete & Continuous Dyn. Sys., 2013, 31(3):797-825. [31] Pesin Y. B., Pitskel' B. S., Topological pressure and the variational principle for noncompact sets, Functional Analysis and Its Applications, 1984, 18(4):307-318. [32] Savkin A. V., Analysis and synthesis of networked control systems:topological entropy, observability, robustness and optimal control, Automatica, 2006, 42(1):51-62. [33] Sun Z., Ge S. S., Switched Linear Systems:Control and Design, Springer-Verlag, London, 2005. [34] Tang J., Li B., Cheng W. C., Some properties on topological entropy of free semigroup action, Dynamical Systems, 2018, 33(1):54-71. [35] Wang Y., Ma D., On the topological entropy of a semigroup of continuous maps, Journal of Mathematical Analysis and Applications, 2015, 427(2):1084-1100. [36] Wang Y., Ma D., Lin X., On the topological entropy of free semigroup actions, Journal of Mathematical Analysis and Applications, 2016, 435(2):1573-1590. [37] Walters P., An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Vol. 79, Springer-Verlag, New York, 1982. [38] Xiong J., Yang Z., Chaos caused by a topological mixing map, In:Shiraiwa K., eds., Proceedings of Advance Series in Dynamical Systems, 1990. [39] Zeng T., Multi-transitivity and Δ-transitivity for semigroup actions, Topology and Its Appl., 2017, 226:1-15. [40] Zhong X., Lü J., Functional envelope of Cantor spaces, Acta Math. Sin., Engl. Series, 2017, 33(3):1-14.
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[1] | 侯成军. 一类Smale空间上的C*-代数自同构的熵[J]. 数学学报, 2017, 60(1): 149-158. | [2] | 杨冰, 侯成军. 双重导子的连续性[J]. Acta Mathematica Sinica, English Series, 2015, 58(5): 853-860. | [3] | 林跃峰. 点度和面度的最小值是3的连通平图[J]. Acta Mathematica Sinica, English Series, 2014, 57(6): 1061-1080. | [4] | 殷允强, 詹建明. 模糊软P-超群[J]. Acta Mathematica Sinica, English Series, 2012, 55(1): 117-130. | [5] | 徐海峰. 方程Δg-aKg=0无正函数解的充分条件[J]. Acta Mathematica Sinica, English Series, 2010, 53(5): 945-952. | [6] | 王肖义;李明军;. 拓扑熵为log 1.618的符号动力系统[J]. Acta Mathematica Sinica, English Series, 2009, (05): 61-66. | [7] | 郭训香;. 自伴算子代数上的某些*-自同态的σ-弱混合性[J]. Acta Mathematica Sinica, English Series, 2007, 50(5): 995-998. | [8] | 张金莲;朱玉峻;何连法. 非自治动力系统的原像熵[J]. Acta Mathematica Sinica, English Series, 2005, 48(4): 693-702. | [9] | 孙太祥. 树映射的不稳定流形,非游荡集与拓扑熵[J]. Acta Mathematica Sinica, English Series, 2002, 45(4): 647-660. | [10] | 曾凡平. 单峰扩张映射的捏制序列[J]. Acta Mathematica Sinica, English Series, 1998, 41(3): -. | [11] | 周作领. 紊动与拓扑熵[J]. Acta Mathematica Sinica, English Series, 1988, 31(1): 83-87. | [12] | 周作领. deg≥2的圆周自映射[J]. Acta Mathematica Sinica, English Series, 1985, 28(2): 200-204. | [13] | 周作领. 线段自映射的通有性质[J]. Acta Mathematica Sinica, English Series, 1984, 27(4): 532-535. |
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