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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) |
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Articles |
[Al] |
Alsedà L. |
Dynamics on Hubbard trees |
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Fundamenta Mathematicae. 164, 115-141. (2000) |
[Be] |
Berliner L.M. |
Statistics, Probability and Chaos |
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Statistical Science. Vol.7 No.1, 69-90. (1992) |
[Br] |
Briggs K. |
A precise calculation of the Feigenbaum constants |
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Mathematics of computation. 57, 435-439. (1991) |
[De1] |
Derrida B. |
Iteration of endomorphisms on the real axis |
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Ann. Inst. Henri Poincaré Vol.29 no.3 305-356. (1978) |
[De2] |
Derrida B. |
Universal metric properties of bifurcations of endomorphisms |
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J. Phys A. 12, 269-296. (1979) |
[Fe1] |
Feigenbaum |
Quantitative Universality for a Class of Nonlinear Transformations |
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J. Stat Phys. 19, 25-52. (1977) |
[Fe2] |
Feigenbaum |
The Universal Metric Properties of Nonlinear Transformations |
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J. Stat Phys. 21, 669-707. (1979) |
[Ka] |
Kaffl A. |
Hubbard Trees and Kneading Sequences for Unicritical and Cubic Polynomials |
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Thesis as part of doctorate. (2006) |
[Li] |
Li & Yorke |
Period Three Implies Chaos |
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Am. Math. Monthly 82, 985. (1975) |
[Ka] |
Kawahira T. |
Notes on Tan's theorem on similarity between M and Jc |
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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 |
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J. Combinatorial theory (A). 15, 25-44. (1971) |
[Pa] |
Pastor G. |
Calculation of the Structure of a Shrub in the Mandelbrot Set |
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Discrete Dynamics in Nature and Society. Vol. 2011 (2011) |
[Sa] |
Sarkovskii A. |
Coexistence of Cycles of a continuous map of a Line into Itself |
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Ukr Mat. Z. 16, 61. (1964) |
[Tr] |
Triennale L. |
The Hausdorff dimension of the boundary of the Mandelbrot set. |
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Thesis as part of doctorate. (2011) |
[Ze] |
Zeng W.-Z. A. |
Scaling properties of period-n-tupling sequences in 1D-mappings |
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Commun. in Theor. Physics (China) Vol.3 No.3, 283-295. (1984) |
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Online |
[Bo] |
Boeing G. |
Chaos theory and the Logistic Map |
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geoffboeing.com/2015/03/chaos-theory-logistic-map/ |
[Bu] |
Burns K. |
The Sharkovsky Theorem: A Natural direct proof (2008) |
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www.math.arizona.edu/~dwang/BurnsHasselblattRevised-1.pdf |
[De3] |
Dewaele N. |
An explanation of period three implies chaos |
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www.siue.edu/~aweyhau/teaching/seniorprojects/dewaele_final.pdf |
[Ka] |
Kartofelev D. |
Lecture on the logistic map and more |
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www.cs.ioc.ee/~dima/YFX1520/Loeng_11.pdf |
[Ki1] |
King C. |
Exploding the Dark Heart of Chaos (2009) |
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www.dhushara.com/DarkHeart/DarkHeart.htm |
[Ki2] |
King C. |
An Intrepid Tour of the Complex Fractal World (2009) |
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www.dhushara.com/DarkHeart/DH.pdf |
[Le] |
Leo & Yorke |
The graph of the logistic map is a tower (2021) |
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https://arxiv.org/pdf/2008.08338.pdf |
[Wo] |
Wolfram |
Logistic Map (from Wolfram MathWorld) |
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https://mathworld.wolfram.com/LogisticMap.html |
[Yo] |
Young P.A. |
The Logistic Map (with Mathematica) |
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physics.ucsc.edu/~peter/242/logistic.pdf |