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对角线传递蕴含按序列对角线分布混沌
Delta Transitivity Implies Delta Distributional Chaos in a Sequence
本文介绍了按序列对角线分布混沌的概念.运用Kuratowski—Mycielski定理，证明了对角线传递系统有稠密的Mycielski按序列对角线分布混沌集.
We introduce the notion of Δ-distributional chaos with respect to a sequence. Using Kuratowski-Mycielski's Theorem, we show that Δ-transitivity implies the existence of a dense Mycielski's set which is Δ-distributional chaotic in some sequence.
对角线传递 / 按序列对角线分布混沌 / 分布混沌 {{custom_keyword}} /
Δ / -transitivity / Δ / -distributional chaos / distributional chaos {{custom_keyword}} /
[1] Akin E., Lectures on Cantor and Mycielski Sets for Dynamical Systems, In:Chapel Hill Ergodic Theory Workshops, Amer. Math. Soc. Providece, RI, 2004, 21-79.
[2] Bernardes N. C., Bonilla A., Peris A., et al., Distributional chaos for operators on banach spaces, J. Math. Anal. Appl., 2018, 459:797-821.
[3] Chen Z. J., Li J., Lü J., Point transitivity, Δ-transitivity and multi-minimality, Ergodic Theory and Dynamical Systems, 2015, 35:1423-1442.
[4] Huang W., Li J., Ye X. D., et al., Positive topological entropy and Δ-weakly mixing sets, Advances in Mathematics, 2017, 306:653-683.
[5] Li J., Li J., Tu S. M., Devaney chaos plus shadowing implies distributional chaos, Chaos, 2016, 26(9):093103, 6 pp.
[6] Li J., Ye X. D., Recent development of chaos theory in topological dynamics, Acta Mathematica Sinica, English Series, 2016, 32(1):83-114.
[7] Li T. Y., Yorke J. A., Period three implies chaos, American Mathematical Monthly, 1975, 82(10):985-992.
[8] Nadler S. B. Jr., Hyperspaces of Sets, Marcel Dekker, New York, 1978, 10-11.
[9] Oprocha P., A note on distributional chaos with respect to a sequence, Nonlinear Analysis Theory Methods & Applications, 2009, 71(11):5835-5839.
[10] Schweizer B., Smítal J., Measures of chaos and a spectral decomposition of dynamical systems on the interval, Transactions of the American Mathematical Society, 1994, 344(2):737-754.
[11] Shao H., Shi Y. M., Zhu H., On distributional chaos in non-autonomous discrete systems, Chaos, Solitons & Fractals, 2018, 107:234-243.
[12] Wang L. P., Yang Y. E., Chu Z. Y., et al., Weakly mixing implies distributional chaos in a sequence, Modern Physics Letters B, 2010, 24(14):1595-1660.
[13] Wang L. P., Huang G. F., Huan D. M., Distributional chaos in a sequence, Nonlinear Analysis Theory Methods & Applications, 2007, 67(7):2131-2136.
[14] Xiong J. C., Lü J., Tan F., Furstenberg family and chaos, Science in China, 2007, 50(9):1325-1333.
[15] Ye X. D., Huang W., Shao S., An Introduction to Topological Dynamical Systems (in Chinese), Science Press, Beijing, 2008, 18.
国家自然科学基金（11771459，11701584，11871228）；广东外语外贸大学研究基金（299-X5218165，299-X5219222）；广东省普通高校特色创新类项目（2018KTSCX122）和广东省基础与应用基础研究基金区域联合基金（青年基金项目：2019A1515110932）
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