Displaying similar documents to “Simple and complex dynamics for circle maps.”

Periods and entropy for Lorenz-like maps

Lluis Alsedà, J. Llibre, M. Misiurewicz, C. Tresser (1989)

Annales de l'institut Fourier

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We characterize the set of periods and its structure for the Lorenz-like maps depending on the rotation interval. Also, for these maps we give the best lower bound of the topological entropy as a function of the rotation interval.

A characterization of the kneading pair for bimodal degree one circle maps

Lluis Alsedà, Antonio Falcó (1997)

Annales de l'institut Fourier

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For continuous maps on the interval with finitely many monotonicity intervals, the kneading theory developed by Milnor and Thurston gives a symbolic description of the dynamics of a given map. This description is given in terms of the kneading invariants which essentially consists in the symbolic orbits of the turning points of the map under consideration. Moreover, this theory also describes a classification of all such maps through theses invariants. For continuous bimodal degree one...

On the topological dynamics and phase-locking renormalization of Lorenz-like maps

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...

Devil's staircase route to chaos in a forced relaxation oscillator

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...