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 circle maps,...
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 of...
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...
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