Attractors of maps of the interval
A. M. Blokh, M. Yu. Lyubich (1989)
Banach Center Publications
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A. M. Blokh, M. Yu. Lyubich (1989)
Banach Center Publications
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Simin Li, Weixiao Shen (2006)
Fundamenta Mathematicae
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It is proved that a smooth unimodal interval map with critical order 2 + ε has no wild attractor if ε >0 is small.
Michael Yampolsky (2003)
Publications Mathématiques de l'IHÉS
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Lluis Alsedà, Jaume Llibre (1989)
Banach Center Publications
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McMullen, Curtis T. (1998)
Documenta Mathematica
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Cowen, Robert (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Andrzej Ehrenfeucht, Edward Grzegorek (1974)
Colloquium Mathematicae
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Jerzy Dydak (1974)
Colloquium Mathematicae
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F. Balibrea, C. La Paz (1997)
Annales Polonici Mathematici
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One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Krystyna Ziemian (1989)
Studia Mathematica
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Sonja Štimac (2006)
Fundamenta Mathematicae
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Using methods of symbolic dynamics, we analyze the structure of composants of the inverse limit spaces of tent maps with finite critical orbit. We define certain symmetric arcs called bridges. They are building blocks of composants. Then we show that the folding patterns of bridges are characterized by bridge types and prove that there are finitely many bridge types.
Jingyal Pak (1978)
Colloquium Mathematicae
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Diogo Baptista, Ricardo Severino (2012)
ESAIM: Proceedings
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Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.
Lluis Alsedà, Antonio Falcó (2003)
Annales de l’institut Fourier
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The aim of this paper is twofold. First we give a characterization of the set of kneading invariants for the class of Lorenz–like maps considered as a map of the circle of degree one with one discontinuity. In a second step we will consider the subclass of the Lorenz– like maps generated by the class of Lorenz maps in the interval. For this class of maps we give a characterization of the set of renormalizable maps with rotation interval degenerate to a rational number, that is, of phase–locking...