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Abstract: Introduction The family of functions f a : R ! R (dependent on the parameter a 2 R) defined by the map x ae f a (x) = a \Gamma x 2 (0.1) has the property that there exist critical values a i of a, at which bifurcations occur in the sets of limit points of sequences fx i g defined by the iteration x i+1 = f a (x i ); i = 0; 1; 2; : : : ; x 0 ! p a: (0.2) If the set of limit points for a given a has n elements, we describe the iteration as having an n-cycle. In other words, the sequence x ... (Update)
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BibTeX entry: (Update)
Briggs, K. M. [1989], `How to calculate the Feigenbaum constants on your PC', Aust. Math Soc. Gazette 16, 89--92. http://citeseer.ist.psu.edu/briggs89how.html More
@article{ briggs89how,
author = "K. M. Briggs",
title = "How to calculate the Feigenbaum constants on your {PC}",
journal = "Aust. Math Soc. Gazette",
volume = "16",
pages = "89--92",
year = "1989",
url = "citeseer.ist.psu.edu/briggs89how.html" }
Citations (may not include all citations):66 Iterated Maps on the Interval as Dynamical System (context) - Collet, Eckmann
35 Quantitative universality for a class of nonlinear transform.. (context) - Feigenbaum - 1978
27 A computer assisted proof of the Feigenbaum conjectures (context) - Lanford - 1982
24 Fundamental limitations for estimating dimensions and Lyapun.. (context) - Eckmann, Ruelle - 1992
21 Etude dynamique des polynomes complexes (context) - Douady, Hubbard - 1986
21 The universal metric properties of nonlinear transformations (context) - Feigenbaum - 1979
19 A method for determining a stochastic transition (context) - Greene - 1979
16 Computer Methods and Borel Summability Applied to Feigenbaum.. (context) - Eckmann, Wittwer - 1985
15 Universality in chaos (context) - Cvitanovi'c - 1984
15 Quasiperiodicity in dissipative systems. A renormalization g.. (context) - Feigenbaum, Kadanoff et al. - 1982
15 Universality in chaos (context) - Cvitanovi'c - 1989
13 Recurrence plots of dynamical systems (context) - Eckmann, Kamphorst et al. - 1987
12 Universal properties of maps on an interval (context) - Collet, Eckmann et al. - 1980
10 A complete proof of the Feigenbaum conjectures (context) - Eckmann, Wittwer - 1987
10 Renormalisation in Area-Preserving Maps (context) - MacKay - 1993
[Article contains additional citations not shown here]
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