Anti-integrability for the Logistic Maps
Anti-integrability for the Logistic Maps
摘要
The embedding of the Bernoulli shift into the logistic map x→μx(1 - x) for μ 〉 4 is reinterpreted by the theory of anti-integrability: it is inherited from the anti-integrable limit μ→∞.
参考文献19
-
1Aubry,S.and Abramovici,G.,Chaotic trajectories in the standard map:the concept of anti-integrability,Phys.D,43,1990,199-219.
-
2Aulbach,B.and Kieninger,B.,An elementary proof for hyperbolicity and chaos of the logistic maps,J.Difference Equ.Appl.,10,2004,1243-1250.
-
3Bolotin,S.V.and MacKay,R.S.,Multibump orbits near the anti-integrable limit for Lagrangian systems,Nonlinearity,10,1997,1015-1029.
-
4Chen,Y.-C.,Anti-integrability in scattering billiards,Dyn.Syst.,19,2004,145-159.
-
5Chen,Y.-C.,Multibump orbits continued from the anti-integrable limit for Lagrangian systems,Regul.Chaotic Dyn.,8,2003,243-257.
-
6Chen,Y.-C.,Bernoulli shift for non-autonomous symplectic twist maps near the anti-integrable limit,Discrete Contin.Dyn.Syst.Ser.B,15,2005,587-598.
-
7Devaney,R.L.,An Introduction to Chaotic Dynamical Systems,Second Edition,Addison-Wesley,New York,1989.
-
8Easton,R.W.,Meiss J.D.and Roberts,G.,Drift by coupling to an anti-integrable limit,Phys.D,156,2001,201-218.
-
9Feigenbaum,M.J.,Quantitative universality for a class of nonlinear transformations,J.5tat.Phys.,19,1978,25-52.
-
10Glendinning,P.,Hyperbolicity of the invariant set for the logistic map with μ> 4,Nonlinear Anal.,47,2001,3323-3332.
-
1丁敏,龚胜波.NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES[J].Acta Mathematica Scientia,2017,37(2):511-526.
-
2范家让,张巨勇.叠层双曲率厚壳静、动态问题的分析解[J].合肥工业大学学报(自然科学版),1990,13(4):1-15.
-
3M.Howard Lee.Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li–Yorke[J].Communications in Theoretical Physics,2014,61(10):485-496.
-
4Xiong Ping DAI.The Density of Linear Symplectic Cocycles with Simple Lyapunov Spectrum in YIC(X, SL(2, R))[J].Acta Mathematica Sinica,English Series,2006,22(1):301-310.
-
5冯存芳,许新建,吴枝喜,汪映海.Synchronization of coupled logistic maps on random community networks[J].Chinese Physics B,2008,17(6):1951-1956.
-
6吴光旭,金元怀.C^n上K-双曲区域与开单位球双全纯等价的充要条件[J].北方工业大学学报,1998,10(1):1-4.
-
7徐瑛,任雪梅,曹彬彬.模糊控制与神经网络相结合的预测研究[J].火炮发射与控制学报,2003,24(2):22-25.
-
8姜海波,李涛,曾小亮,张丽萍.Bifurcation analysis of the logistic map via two periodic impulsive forces[J].Chinese Physics B,2014,23(1):112-118.
-
9张鹏,戴世强,刘儒勋.DESCRIPTION AND WENO NUMERICAL APPROXIMATION TO NONLINEAR WAVES OF A MULTI-CLASS TRAFFIC FLOW LWR MODEL[J].Applied Mathematics and Mechanics(English Edition),2005,26(6):691-699.
-
10Bei Ye FENG.A Trick Formula to Illustrate the Period Three Bifurcation Diagram of the Logistic Map[J].Journal of Mathematical Research and Exposition,2010,30(2):286-290. 被引量:1