Two-parameter families of discontinuous one-dimensional maps
Abstract
The aim of this paper is to establish the existence of a "box-within-a-box" bifurcation structure for monotone families of Lorenz maps and to study its combinatorics.
References
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2. J. Guckenheimer, R.F. Williams, Structure Stability of Lorenz Attractors, Publ. Math. IHES (1979), 59-72.
3. I. Gumovski, C. Mira, Dynamique Chaotique, Cepadues Editions, 1980.
4. J.H. Hubbard, C.T. Sparrow, The Classification of Topologically Expansive Lorenz Maps, Comm. on Pure and Appl. Math. 43 (1990), 431-443.
5. M. Martens, W. De Melo, Universal Models for Lorenz Maps, Preprints of SUNY at Stony Brook, 1996.
6. W. de Melo, S. van Strien, One Dimensional Dynamics, Springer-Verlag, Berlin and New York, 1993.
7. J. Milnor, W. Thurston, On Iterated Maps of the Interval, Lecture Notes in Math. 1342, Springer, 1988, 465-563.
8. D. Singer, Stable Orbits and Bifurcations of Maps of the Interval, SIAM. J. Appl. Math. 35 (1978), 260-267.
9. D. Rand, The Topological Classification of Lorenz Attractors, Math. Proc. Cambridge Philos. Soc. 83 (1978), 451-460.
SilvaL., & Sousa RamosJ. (1999). Two-parameter families of discontinuous one-dimensional maps. Annales Mathematicae Silesianae, 13, 257-270. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14154
Luis Silva
lfs@dmat.uevora.pt
Departamento de Matemática Universidade de Évora, Portugal Portugal
Departamento de Matemática Universidade de Évora, Portugal Portugal
José Sousa Ramos
Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal Portugal
Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal Portugal
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