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  • 1.Nonlinear systems
    2.One-dimensional maps
    3.The logistic map
    4.Fractal geometry
    5.The Mandelbrot set
    6.Multidimensional maps
    7.Continuous systems
    8.Dissipative systems
    9.Conservative systems


    Nonlinear systems



    One-dimensional maps



    The logistic map




    Fractal geometry



    The Mandelbrot set



    Multi-dimensional maps



    Continuous systems



    Dissipative systems



    Conservative systems


    References

    Books
    [Ca] Carleson L. Complex Dynamics (1996)
    [Co] Collet P. Iterated Maps on the Interval as Dynamical Systems (1980)
    [Cv] Cvitanović P. Universality in Chaos (1989)
    [De1] Devaney R. An Introduction to Chaotic Dynamical systems (1989)
    [De2] Devaney R. Complex Dynamical Systems AMS, Proceedings of Symposia Vol.49 (1994)
    [Fa1] Falconer K. The Geometry of Fractal Sets (1985)
    [Fa2] Falconer K. Fractal Geometry (1990)
    [Fi] Finch S. Mathematical constants (2003)
    [Gl] Gleick J. Chaos (1987)
    [Ma1] Mandelbrot B. The Fractal Geometry of Nature (1982)
    [Ma2] Mandelbrot B. Fractals and Chaos (2004)
    [Oh] Ohlén G. Chaos (2007)
    [Ot] Ott E. Chaos in Dynamical Systems (2002)
    [Pe1] Peitgen H.-O. The Beauty of Fractals (1986)
    [Pe2] Peitgen H.-O. Chaos and Fractals (2004)
    [Ra] Rasband S. Chaotic Dynamics of Nonlinear Systems (1990)
    [Sc1] Schleicher D. Complex Dynamics (2009)
    [Sc2] Schuster H. G. Deterministic Chaos (1988)
     
    Articles
    [Al] Alsedà L. Dynamics on Hubbard trees
    Fundamenta Mathematicae. 164, 115-141. (2000)
    [Be] Berliner L.M. Statistics, Probability and Chaos
    Statistical Science. Vol.7 No.1, 69-90. (1992)
    [Br] Briggs K. A precise calculation of the Feigenbaum constants
    Mathematics of computation. 57, 435-439. (1991)
    [De1] Derrida B. Iteration of endomorphisms on the real axis
    Ann. Inst. Henri Poincaré Vol.29 no.3 305-356. (1978)
    [De2] Derrida B. Universal metric properties of bifurcations of endomorphisms
    J. Phys A. 12, 269-296. (1979)
    [Fe1] Feigenbaum Quantitative Universality for a Class of Nonlinear Transformations
    J. Stat Phys. 19, 25-52. (1977)
    [Fe2] Feigenbaum The Universal Metric Properties of Nonlinear Transformations
    J. Stat Phys. 21, 669-707. (1979)
    [Ka] Kaffl A. Hubbard Trees and Kneading Sequences for Unicritical and Cubic Polynomials
    Thesis as part of doctorate. (2006)
    [Li] Li & Yorke Period Three Implies Chaos
    Am. Math. Monthly 82, 985. (1975)
    [Ka] Kawahira T. Notes on Tan's theorem on similarity between M and Jc
    Part of paper on Zalcman function and similarity beteen M and Jc (2019)
    [Me] Metropolis N. On Finite Limit Sets for Transformations on the Unit interval
    J. Combinatorial theory (A). 15, 25-44. (1971)
    [Pa] Pastor G. Calculation of the Structure of a Shrub in the Mandelbrot Set
    Discrete Dynamics in Nature and Society. Vol. 2011 (2011)
    [Sa] Sarkovskii A. Coexistence of Cycles of a continuous map of a Line into Itself
    Ukr Mat. Z. 16, 61. (1964)
    [Tr] Triennale L. The Hausdorff dimension of the boundary of the Mandelbrot set.
    Thesis as part of doctorate. (2011)
    [Ze] Zeng W.-Z. A. Scaling properties of period-n-tupling sequences in 1D-mappings
    Commun. in Theor. Physics (China) Vol.3 No.3, 283-295. (1984)
     
    Online
    [Bo] Boeing G. Chaos theory and the Logistic Map
    geoffboeing.com/2015/03/chaos-theory-logistic-map/
    [Bu] Burns K. The Sharkovsky Theorem: A Natural direct proof (2008)
    www.math.arizona.edu/~dwang/BurnsHasselblattRevised-1.pdf
    [De3] Dewaele N. An explanation of period three implies chaos
    www.siue.edu/~aweyhau/teaching/seniorprojects/dewaele_final.pdf
    [Ka] Kartofelev D. Lecture on the logistic map and more
    www.cs.ioc.ee/~dima/YFX1520/Loeng_11.pdf
    [Ki1] King C. Exploding the Dark Heart of Chaos (2009)
    www.dhushara.com/DarkHeart/DarkHeart.htm
    [Ki2] King C. An Intrepid Tour of the Complex Fractal World (2009)
    www.dhushara.com/DarkHeart/DH.pdf
    [Le] Leo & Yorke The graph of the logistic map is a tower (2021)
    https://arxiv.org/pdf/2008.08338.pdf
    [Wo] Wolfram Logistic Map (from Wolfram MathWorld)
    https://mathworld.wolfram.com/LogisticMap.html
    [Yo] Young P.A. The Logistic Map (with Mathematica)
    physics.ucsc.edu/~peter/242/logistic.pdf