Hunting Admissible Kneading pairs of a Real Rational Map
Keywords:
Symbolic Dynamics, Real Rational Maps, Kneading TheoryAbstract
The importance of symbolic systems is that they give us the possibility of simplifying some dynamical systems. Our expectations is that our work can help to understand better the behavior, under iteration, of the Real Rational Map, f(x)=(x²-a)/(x²-b), with 0<b<a<1. Kneading Theory is a powerful tool, and we use it to simplify processes arising from the complicated behavior of this map in a more simple way. In this work we establish some rules that bound regions where we can find, or not, Kneading pairs for f(x).
References
Adler, R.L., “Symbolic dynamics and Markov partitions. Bull.Amer.Math. Soc.â€, vol. 35, no. 1, pp. 1-56,1998
Cabral, J., “Symbolic Dynamics for Real Rational Mapsâ€, Asian Journal of Fuzzy and Applied Mathematics, Vol.1, no. 4, December 2013.
Marcus, B., “Symbolic dynamics and connections to coding theory, automata theory and system theoryâ€, In Proceedings of Symposia in Applied Mathematics, vol. 50, pp. 95-108. 1995
Martins N., Severino R., and Sousa Ramos J., “Isentropic real cubic mapsâ€, Internat. J. Bifur. Chaos Appl. Sci. Engr., vol. 13, no. 7, pp. 1701-1709,2001.
Milnor J., Thurston W., “On iterated maps of the intervalâ€, In Dynamical Systems proc. Univ. Maryland 1986-87, pp. 465-563, Lect. Notes in Math., Springer-Verlag, 1988.
Ramos, C. Correia, “Representações, Ãlgebras C* e Transformações do intervaloâ€, Phd Thesis, Technical University of Lisbon, 2006
Sousa Ramos, J. “Hiperbolicidade e Bifurcação de Sistemas Simbólicosâ€, Phd Thesis, Technical University of Lisbon, 1989
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