Currently displaying 1 – 13 of 13

Showing per page

Order by Relevance | Title | Year of publication

Dynamics on Hubbard trees

Lluís AlsedàNúria Fagella — 2000

Fundamenta Mathematicae

It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type....

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

Lluis AlsedàAntonio Falcó — 1997

Annales de l'institut Fourier

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,...

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

Lluis AlsedàAntonio Falcó — 1994

Annales de l'institut Fourier

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...

Simple and complex dynamics for circle maps.

Lluís AlsedàVladimir Fedorenko — 1993

Publicacions Matemàtiques

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.

Rotation sets for graph maps of degree 1

Lluís AlsedàSylvie Ruette — 2008

Annales de l’institut Fourier

For a continuous map on a topological graph containing a loop S it is possible to define the degree (with respect to the loop S ) and, for a map of degree 1 , rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop S then the set of rotation numbers of points in S has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational...

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

Lluis AlsedàAntonio Falcó — 2003

Annales de l’institut Fourier

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...

On the definition of strange nonchaotic attractor

Lluís AlsedàSara Costa — 2009

Fundamenta Mathematicae

The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove that a whole...

On the primary orbits of star maps (first part)

Lluis AlsedàJose Miguel Moreno — 2002

Applicationes Mathematicae

This paper is the first one of a series of two, in which we characterize a class of primary orbits of self maps of the 4-star with the branching point fixed. This class of orbits plays, for such maps, the same role as the directed primary orbits of self maps of the 3-star with the branching point fixed. Some of the primary orbits (namely, those having at most one coloured arrow) are characterized at once for the general case of n-star maps.

On the preservation of combinatorial types for maps on trees

Lluís AlsedàDavid JuherPere Mumbrú — 2005

Annales de l'institut Fourier

We study the preservation of the periodic orbits of an A -monotone tree map f : T T in the class of all tree maps g : S S having a cycle with the same pattern as A . We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of f into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved.

All solenoids of piecewise smooth maps are period doubling

Lluís AlsedàVíctor Jiménez LópezL’ubomír Snoha — 1998

Fundamenta Mathematicae

We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if p 1 < . . . < p n is a periodic orbit of a continuous map f then there is a union set q 1 , . . . , q n - 1 of some periodic orbits of f such that p i < q i < p i + 1 for any i.

Page 1

Download Results (CSV)