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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) |
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|
Articles |
[14] |
Berliner L.M. |
Statistics, Probability and Chaos |
|
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Statistical Science. Vol.7 No.1, 69-90. (1992) |
[15] |
Briggs K. |
A precise calculation of the Feigenbaum constants |
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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 |
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J. Phys A. 12, 269-296. (1979) |
[18] |
Feigenbaum M. |
Quantitative Universality for a Class of Nonlinear Transformations |
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J. Stat Phys. 19, 25-52. (1977) |
[19] |
Feigenbaum M. |
The Universal Metric Properties of Nonlinear Transformations |
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J. Stat Phys. 21, 669-707. (1979) |
[20] |
Li T. and Yorke J. |
Period Three Implies Chaos |
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Am. Math. Monthly 82, 985. (1975) |
[21] |
Metropolis N. et al. |
On Finite Limit Sets for Transformations on the Unit interval |
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J. Combinatorial theory (A). 15, 25-44. (1971) |
[22] |
Sarkovskii A. |
Coexistence of Cycles of a continuous map of a Line into Itself |
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Ukr Mat. Z. 16, 61. (1964) |
[23] |
Zeng W.-Z. A. et al. |
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 |
[24] |
Boeing G. |
Chaos theory and the Logistic Map |
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|
geoffboeing.com/2015/03/chaos-theory-logistic-map/ |
[25] |
Burns K. et al. |
The Sharkovsky Theorem: A Natural direct proof (2008) |
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|
www.math.arizona.edu/~dwang/BurnsHasselblattRevised-1.pdf |
[26] |
Dewaele N. |
An explanation of period three implies chaos |
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|
www.siue.edu/~aweyhau/teaching/seniorprojects/dewaele_final.pdf |
[27] |
Kartofelev D. |
Lecture on the logistic map and more |
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|
www.cs.ioc.ee/~dima/YFX1520/Loeng_11.pdf |
[28] |
Leo R. & Yorke J. |
The graph of the logistic map is a tower (2021) |
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|
https://arxiv.org/pdf/2008.08338.pdf |
[29] |
Wolfram |
Logistic Map (from Wolfram MathWorld) |
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|
https://mathworld.wolfram.com/LogisticMap.html |
[30] |
Young P.A. |
The Logistic Map (with Mathematica) |
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|
physics.ucsc.edu/~peter/242/logistic.pdf |