Symbolic dynamics of bimodal maps.
Lampreia, J.P., Sousa Ramos, J. (1997)
Portugaliae Mathematica
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Lampreia, J.P., Sousa Ramos, J. (1997)
Portugaliae Mathematica
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J. P. Lampreia, A. Rica da Silva, J. Sousa Ramos (1988)
Stochastica
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In this paper we introduce a ⊗-operation over Markov transition matrices, in the context of subshift of finite type, reproducing symbolic properties of the iterates of the critical point on a one-parameter family of unimodal maps. To the *-product between kneading sequences we associate a ⊗-product between the corresponding Markov matrices.
Martins, Nuno, Severino, Ricardo, Sousa Ramos, J. (2003)
International Journal of Mathematics and Mathematical Sciences
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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.
Shultz, Fred (2005)
The New York Journal of Mathematics [electronic only]
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Franz Hofbauer, Gerhard Keller (1990)
Annales de l'I.H.P. Physique théorique
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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...
Alsedà, Ll., Mañosas, F. (1996)
Acta Mathematica Universitatis Comenianae. New Series
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Rafael Labarca, Carlos Gustavo Moreira (2006)
Annales de l'I.H.P. Analyse non linéaire
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