簡單通往複雜之路

20170115第十一期

科學家對成長函數超過一甲子的狂熱

作者:班榮超

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          • 作者簡介
            班榮超為東華大學應用數學系教授,主要研究領域為微分方程、動力系統、遍歷理論。
          • 本文出處
            本文主要內容為2016 年4 月9 日作者在臺灣大學科學教育發展中心「秩序與複雜的華爾滋」系列講座的演講稿,並做增補而成。
          • 延伸閱讀
            ◊ 班榮超〈簡單的開始,卻通往複雜?!〉(2016/4/9),CASE探索《秩序與複雜的華爾滋》系列講座第二講錄影:https://youtu.be/fBdD0PIIIaQ
            ◊ T.-Y. Li & Yorke, James “Period Three Implies Chaos” The American Mathematical monthly 82 (1975) no.10。李天岩和Yorke 的經典論文,發表在相對平易近人的AMM 雜誌,只要會大學微積分就能讀懂。http://goo.gl/N0ZH4d
            ◊ 李天岩〈關於”Li-Yorke 混沌” 的故事〉(1988),《數學傳播》第12 卷第3 期。可以看到這項發現無心插柳的有趣故事,網路版請見:link 也可參看http://episte.math.ntu.edu.tw/articles/mm/mm_12_3_02/
          • 參考資料
            [1] Georg Cantor  “Über unendliche, lineare Punktmannigfaltigkeiten V” [On infinite, linear point-manifolds (sets)](1883),●[斜]Mathematische Annalen●, vol. 21, pp. 545–591.
            [2]  Aristid Lindenmayer, “Mathematical models for cellular interaction in development.” ●[斜]J. Theoret. Biology●, 18:280—315, 1968.
            [3]  Feigenbaum, M. J. “Quantitative Universality for a Class of Non-Linear Transformations.” ●[斜]J. Stat. Phys.●19, 25-52, 1978.
            [4] John Milnor and William Thurston, “On iterated maps of the interval. Dynamical systems” (College Park, MD, 1986–87)●[斜], ●[斜]Lecture Notes in Math.●, 1342, 465–563, Springer, Berlin, 1988
            [5] T.Y. Li, and J.A. Yorke, “Period Three Implies Chaos”, ●[斜]American Mathematical Monthly●[斜] 82, 985 (1975)
            [6] A.N. Sharkovskii, “Co-existence of cycles of a continuous mapping of the line into itself”, ●[斜]Ukrainian Math. J.●, 16:61-71 (1964).
            [7]Robert L. Devaney,  ●[斜]An Introduction to Chaotic Dynamical Systems● (Benjamin/Cummings 1986; 2nd ed., Addison-Wesley, 1989; reprinted by Westview Press, 2003)
            [8] J. Banks, J. Brooks, G. Cairns, G. Davis and P. Stacey , “On Devaney’s Definition of Chaos”, ●[斜]The American Mathematical Monthly●, Vol. 99, No. 4 (Apr., 1992), pp. 332-334
            [9] Wen Huang and Xiangdong Ye, “Devaney’s chaos or 2-scattering implies Li-Yorke chaos”, ●[斜]Topology and its Application●, vol 17(3), pp.259-272.
            [10] Erdös, Paul; Turán, Paul, “On some sequences of integers” (1936), ●[斜]Journal of the London Mathematical Society●. Vol. 11?(4), pp. 261–264.
            [11] Szemerédi, Endre,”On sets of integers containing no k elements in arithmetic progression”(1975), ●[斜]Acta Arithmetica●, Vol. 27, pp. 199–245.
            [12] Green, Ben,  Tao, Terence , “The primes contain arbitrarily long arithmetic progressions” (2008), ●[斜]Annals of Mathematics●[斜].Vol. 167(2), pp. 481–547.
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