Kneading theory of Lorenz maps
Lluis Alsedà, Jaume Llibre (1989)
Banach Center Publications
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Lluis Alsedà, Jaume Llibre (1989)
Banach Center Publications
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Lluis Alsedà, Antonio Falcó (1994)
Annales de l'institut Fourier
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We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance...
Tomasz Nowicki (1985)
Fundamenta Mathematicae
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J. Palis (2005)
Annales de l'I.H.P. Analyse non linéaire
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Mark Pollicott (2009)
Fundamenta Mathematicae
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We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
A. M. Blokh, M. Yu. Lyubich (1989)
Banach Center Publications
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Andrew D. Barwell, Chris Good, Piotr Oprocha (2012)
Fundamenta Mathematicae
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We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.
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.
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...
Xavier Buff, Thomas Gauthier (2013)
Bulletin de la Société Mathématique de France
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We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.