Displaying similar documents to “Periods and entropy for Lorenz-like maps”

Simple and complex dynamics for circle maps.

Lluís Alsedà, Vladimir Fedorenko (1993)

Publicacions Matemàtiques

Similarity:

The continuous self maps of a closed interval of the real line with zero topological entropy can be characterized in terms of the dynamics of the map on its chain recurrent set. In this paper we extend this characterization to continuous self maps of the circle. We show that, for these maps, the chain recurrent set can exhibit a new dynamic behaviour which is specific of the circle maps of degree one.

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

Lluis Alsedà, Antonio Falcó (1997)

Annales de l'institut Fourier

Similarity:

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...

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

Lluis Alsedà, Antonio Falcó (1994)

Annales de l'institut Fourier

Similarity:

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...