贾诺;王涛;

• 1:哈尔滨师范大学数学科学学院

摘要(Abstract)：

利用拓扑和遍历理论对Devaney混沌意义下变换的弱混合与拓扑混合、拓扑传递及初值敏感的关系进行了研究,改进了已有文献的结论,证明了弱混合则初值敏感.

关键词(KeyWords)： 保测变换;弱混合;拓扑传递;初值敏感

Abstract:

Keywords:

基金项目(Foundation): 黑龙江省教育厅科学技术研究项目(12541243);; 哈尔滨师范大学青年学术骨干资助计划研究项目(KGB201222)

作者(Authors): 贾诺;王涛;

参考文献(References)：

• [1]Devaney R.An Introduction to Chaotic Dynamical Systems[M].Boston:Addison-Wesley,1989.
• [2]Banasiak J,Lachowicz M,Moszynski M.Topological Chaos:When Topology Meets Medicine[J].Appl.Math.Lett.,2003,16(3):306-308.
• [3]Khan M A,Mitra T.On topological chaos in the Robinson-Solow-Srinivasan model[J].Econom.Lett.,2005,88(1):127-133.
• [4]Finn M D,Thiffeault J L,Gouillart E.Topological chaos in spatially periodic mixers[J].Phys.D,2006,221(1):92-100.
• [5]Wei L,Ruan J.Chaotic dynamics of an integrate-and-fire circuit with periodic pulse-train input[J].IEEETrans.Circuits Syst.I,2003,50(5):686-778.
• [6]Akhmet M U.Devaney’s chaos of a relay system[J].Commun.Nonlinear Sci.Numer.Simul.,2009,14(4):1486-1493.
• [7]Rudnicki R.Chaos for some infinite-dimensional dynamical systems[J].Math.Methods Appl.Sci.,2004,27(6):723-738.
• [8]Banks J,Brooks J,Cairns G.et al.On Devaney’s definition of chaos[J].Amer.Math.Monthly,1992,99(4):332-334.
• [9]Vellekoop M,Bergllund R.On intervals,transitivity=chaos[J].Amer.Math.Monthly,1994,101(4):353-355.
• [10]Syahida C D,Good C.On Devaney Chaos and Dense Periodic Points:Period 3 and Higher Implies Chaos[J].Amer.Math.Monthly,2015,122(8):773-780.
• [11]Pollicott M,Yuri M.Dynamical Systems and Ergodic Theory[M].Cambridge:Cambridge University Press,1998.
• [12]Peter W.An Introduction to Ergodic Theory[M].Berlin:Springer,1981.
• [13]Akin E.The General Topology of Dynamical Systems[M].Providence:American Mathematical Society,1993.
• [14]Grosse-Erdman K G,Manguillot A P.Linear Chaos[M].Berlin:Springer,2011.
• [15]Xu Z J,Lin W,Ruan J.Decay of correlations implies chaos in the sense of Devaney[J].Chaos Solitons Fractals,2004,22(2):305-310.
• [16]Salim L.On some stochastic properties in Devaney’s chaos[J].Chaos Solitons Fractals,2006,28(3):668-672.
• [17]王涛,贾诺.Devaney混沌的随机性质[J].数学的实践与认识,2010,40(7):210-213.
• [18]England J W,Martin N F B.On weak mixing metric automorphisms[J].Bull.Amer.Math.Soc.,1968,74(3):505-507.
• [19]Halmos P R.Lectures on Ergodic Theory[M].Chelsea,New York,1956.
• [20]Rom′an-Flores H,Chalco-Cano Y.Some chaotic properties of Zadeh’s extension[J].Chaos Solitons Fractals,2008,35(3):452-459.
• [21]Kupka J.On Devaney chaotic induced fuzzy and set-valued dynamical systems[J].Fuzzy Sets and Systems,2011,177(1):34-44.
• [22]Kupka J.On fuzzifications of discrete dynamical systems[J].Inform.Sci.,2011,181(13):2858-2872.
• [23]Lan Y,Li Q,Mu C,et al.Some chaotic properties of discrete fuzzy dynamical systems[J].Abstr.Appl.Anal.,2012,Article ID 875381,9 pages.