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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
    [1] Collet P. et al. Iterated Maps on the Interval as Dynamical Systems (1980)
    [2] Cvitanović P. Universality in Chaos (1989)
    [3] Devaney R. An Introduction to Chaotic Dynamical systems (1989)
    [4] Falconer K. The Geometry of Fractal Sets (1985)
    [5] Falconer K. Fractal Geometry (1990)
    [6] Finch S. Mathematical constants (2003)
    [7] Gleick J. Chaos (1987)
    [8] Mandelbrot B. The Fractal Geometry of Nature (1982)
    [9] Ohlén G. et al. Chaos (2007)
    [10] Ott E. Chaos in Dynamical Systems (2002)
    [11] Peitgen H.-O. et al. The Beauty of Fractals (1986)
    [12] Rasband S. Chaotic Dynamics of Nonlinear Systems (1990)
    [13] Schuster H. G. Deterministic Chaos (1988)
     
    Articles
    [14] Berliner L.M. Statistics, Probability and Chaos
    Statistical Science. Vol.7 No.1, 69-90. (1992)
    [15] Briggs K. A precise calculation of the Feigenbaum constants
    Mathematics of computation. 57, 435-439. (1991)
    [16] Derrida B. et al. Iteration of endomorphisms on the real axis and representation of numbers
    Ann. Inst. Henri Poincaré Vol.29 no.3 305-356 (1978)
    [17] Derrida B. et al. Universal metric properties of bifurcations of endomorphisms
    J. Phys A. 12, 269-296. (1979)
    [18] Feigenbaum M. Quantitative Universality for a Class of Nonlinear Transformations
    J. Stat Phys. 19, 25-52. (1977)
    [19] Feigenbaum M. The Universal Metric Properties of Nonlinear Transformations
    J. Stat Phys. 21, 669-707. (1979)
    [20] Li T. and Yorke J. Period Three Implies Chaos
    Am. Math. Monthly 82, 985. (1975)
    [21] Metropolis N. et al. On Finite Limit Sets for Transformations on the Unit interval
    J. Combinatorial theory (A). 15, 25-44. (1971)
    [22] Sarkovskii A. Coexistence of Cycles of a continuous map of a Line into Itself
    Ukr Mat. Z. 16, 61. (1964)
    [23] Zeng W.-Z. A. et al. Scaling properties of period-n-tupling sequences in 1D-mappings
    Commun. in Theor. Physics (China) Vol.3 No.3, 283-295. (1984)
     
    Online
    [24] Boeing G. Chaos theory and the Logistic Map
    geoffboeing.com/2015/03/chaos-theory-logistic-map/
    [25] Burns K. et al. The Sharkovsky Theorem: A Natural direct proof (2008)
    www.math.arizona.edu/~dwang/BurnsHasselblattRevised-1.pdf
    [26] Dewaele N. An explanation of period three implies chaos
    www.siue.edu/~aweyhau/teaching/seniorprojects/dewaele_final.pdf
    [27] Kartofelev D. Lecture on the logistic map and more
    www.cs.ioc.ee/~dima/YFX1520/Loeng_11.pdf
    [28] Leo R. & Yorke J. The graph of the logistic map is a tower (2021)
    https://arxiv.org/pdf/2008.08338.pdf
    [29] Wolfram Logistic Map (from Wolfram MathWorld)
    https://mathworld.wolfram.com/LogisticMap.html
    [30] Young P.A. The Logistic Map (with Mathematica)
    physics.ucsc.edu/~peter/242/logistic.pdf