Non-uniformly expanding dynamics in maps with singularities and criticalities
Stephano Luzzatto, Warwick Tucker (1999)
Publications Mathématiques de l'IHÉS
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Stephano Luzzatto, Warwick Tucker (1999)
Publications Mathématiques de l'IHÉS
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Bladismir Leal (2008)
Annales de l'I.H.P. Analyse non linéaire
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Michael Yampolsky (2003)
Publications Mathématiques de l'IHÉS
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Karen Brucks, R. Galeeva, P. Mumbrú, D. Rockmore, Charles Tresser (1997)
Fundamenta Mathematicae
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We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.
Gregory J. Davis (1990)
Publicacions Matemàtiques
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In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.
Tomasz Nowicki (1985)
Fundamenta Mathematicae
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Andres, Jan (2005)
Fixed Point Theory and Applications [electronic only]
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Mikhail Lyubich, Michael Yampolsky (1997)
Annales de l'institut Fourier
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We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map , , is locally connected.
Andres, Jan, Górniewicz, Lech (2006)
Fixed Point Theory and Applications [electronic only]
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