An Approach to the Ordering of One-Dimensional Quadratic Maps

Chaos, Solitons and Fractals

Volumn 7, Issue 4 SPEC. ISS., 1996, Pages 565-584

  Pastor, G ^a   Romera, M ^a   Montoya, F ^a  

^a Consejo Superior de Investigaciones Científicas   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038284973     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/0960-0779(95)00071-2     Document Type: Article

References (24)

1. D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20, 167-192 (1971).
2. K. R. Sheenivasan, in Frontiers in Fluid Mechanics, edited by J. J. Lumley. Springer, Berlin (1985).
3. J. P. Crutchfield and K. Kaneko, in Directions in Chaos, edited by Hao Bai-Lin, Vol. II. World-Scientific, Singapore (1987) and references therein.
4. T. Screiber, Spatio-temporal structure in coupled map lattices: two points correlations versus mutual information, J. Phys. A 23, L393 (1990).
5. M. Romera, G. Pastor, J. Negrillo and F. Montoya, in Fractals in the Natural and Applied Science, edited by M. M. Novak. Chapman & Hall, London (1995).
6. M. Romera, G. Pastor and F. Montoya, Graphic tools to analyse one-dimensional quadratic maps, Computer & Graphics 20 (1996), in press.
7. J. Milnor and W. Thurston, On iterated maps of the interval, Lecture Notes in Math. 1342, 465-563 (1988).
8. B. B. Mandelbrot, Fractals aspects of the iteration of z → λz(1 - z) for complex λ and z, in Nonlinear Dynamics, edited by R. H. G. Helleman, Ann. NY Acad. Sci. 357, 249-259 (1980).
9. 2 - μ for complex μ and z: the fractal structure of its M set, and scaling, Physica 7, 224-239 (1983).
10. B. Branner, The Mandelbrot set, Proc. Symposia Appl. Math. 39, 75-105 (1989).
11. J. Hale and H. Koçak, Dynamics and Bifurcations. Springer, New York (1991).
12. N. Metropolis, M. L. Stein and P. R. Stein, On finite limit sets for transformations on the unit interval, Journal of Combinatorial Theory 15, 25-44 (1973).
13. M. Lutzky, Counting hyperbolic components of the Mandelbrot set, Physics Letters A 177, 338-340 (1993).
14. F. Xie and B. Hao, Counting the number of periods in one-dimensional maps with multiple critical points, Physica A 202, 237-263 (1994).
15. A. N. Sharkovsky, Coexistence of cycles of a continuous transformation of a line into itself, Ukrain. Mat. Zhurn 16, 61-71 (Russian) (1964).
16. A. N. Sharkovsky, Yu. L. Maistrenko and E. Yu. Romanenko, Difference Equations and Their Applications. Kluwer Academic Publishers, Dordrecht (1993).
17. T. Y. Li and J. A. Yorke, Period three implies chaos, Am. Math. Monthly 82, 985-992 (1975).
18. M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Memoirs of the Am. Math. Soc. 94(465), (1991).
19. A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes, Publications Mathematiques D'Orsay 84-02, Université de Paris-Sud (1984).
20. A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. Ecole Norm. Sup. 18, 287-344 (1985).
21. H. O. Peitgen, H. Jürgens and D. Saupe, Chaos and Fractals. Springer, New York (1992).
22. M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, Journal of Statistical Physics 19, 25-52 (1978).
23. H. O. Peitgen and D. Saupe (eds), The Science of Fractal Images. Springer, New York (1988).
24. T. Post and H. W. Capel, Windows in one-dimensional maps, Physica A 178, 62-100 (1991).