Symbolic Dynamics for Real Rational Maps
Keywords:Rational maps, symbolic dynamics, topological entropy, Markov partitions
This work is an attempt to study the dynamics of real rational maps f ab (x) = (x 2 - a) / (x 2 - b), using symbolic dynamics. It is given an example that illustrates how the topological entropy can be calculated using kneading theory and Markov partitions in this family of rational maps.
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Milnor, J. and Thurston, W., â€œOn Iterated Maps of the Intervalâ€, In J.C. Alexander (ed.) Proceedings Univ. Maryland 1986-1987. Lect. Notes in Math. 1342, pp. 465-563, Springer-Verlag, berlin-New York, 1988.
Ramos, J.S., â€œHiperbolicidade e BifurcaÃ§Ã£o de Sistemas SimbÃ³licosâ€, PhD. Thesis, Universidade de Lisboa, available at http://purl.pt/7368, 1989
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