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    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/121187


    Title: Multidimensional dynamics: from simple to complicated
    Authors: Liao, Kang-Ling
    Shih, Chih-Wen
    曾睿彬
    Tseng, Jui-Pin
    Contributors: 應數系
    Date: 2011-04
    Issue Date: 2018-12-04 11:20:03 (UTC+8)
    Abstract: The most apparent look of a discrete-time dynamical system is that an orbit is composed of a collection of points in phase space, in contrast to a trajectory curve for a continuous-time system. A basic and prominent theoretical difference between discrete-time and continuous-time dynamical systems is that chaos occurs in one-dimensional discrete-time dynamical systems, but not for one-dimensional deterministic continuous-time dynamical systems; the logistic map and logistic equation are the most well-known example illustrating this difference. On the one hand, fundamental theories for discrete-time systems have also been developed in a parallel manner as for continuous-time dynamical systems, such as stable manifold theorem, center manifold theorem and global attractor theory etc. On the other hand, analytical theory on chaotic dynamics has been developed more thoroughly for discrete-time systems (maps) than for continuous-time systems. Li-Yorke’s period-three-implies-chaos and Sarkovskii’s ordering on periodic orbits for one-dimensional maps are ones of the most celebrated theorems on chaotic dynamics.
    Relation: Discrete Time Systems, InTech, pp.505-526
    Data Type: book/chapter
    DOI 連結: http://dx.doi.org/10.5772/15320
    DOI: 10.5772/15320
    Appears in Collections:[俄羅斯研究所] 專書/專書篇章

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