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題名:	Multidimensional dynamics: from simple to complicated
作者:	Liao, Kang-Ling Shih, Chih-Wen 曾睿彬 Tseng, Jui-Pin
貢獻者:	應數系
日期:	2011-04
上傳時間:	2018-12-04 11:20:03 (UTC+8)
摘要:	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.
關聯:	Discrete Time Systems, InTech, pp.505-526
資料類型:	book/chapter
DOI 連結:	http://dx.doi.org/10.5772/15320
DOI:	10.5772/15320
顯示於類別:	[俄羅斯研究所] 專書/專書篇章

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