Displaying similar documents to “On stability of forcing relations for multidimensional perturbations of interval 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.

Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two

W. Ingram, Robert Roe (1999)

Colloquium Mathematicae

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We derive several properties of unimodal maps having only periodic points whose period is a power of 2. We then consider inverse limits on intervals using a single strongly unimodal bonding map having periodic points whose only periods are all the powers of 2. One such mapping is the logistic map, f λ ( x ) = 4λx(1-x) on [f(λ),λ], at the Feigenbaum limit, λ ≈ 0.89249. It is known that this map produces an hereditarily decomposable inverse limit with only three topologically different subcontinua....

Simple and complex dynamics for circle maps.

Lluís Alsedà, Vladimir Fedorenko (1993)

Publicacions Matemàtiques

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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.

On the ∗-product in kneading theory

Karen Brucks, R. Galeeva, P. Mumbrú, D. Rockmore, Charles Tresser (1997)

Fundamenta Mathematicae

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We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit 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...