Symbolic Dynamics for Real Rational Maps


  • João Cabral Azores University


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.

Author Biography

João Cabral, Azores University

Assistant Teacher

Maths Department


Lampreia, J.P. and Ramos, J.S., “Symbolic Dynamics of Bimodal Mapsâ€, In Portugaliae Mathematica, vol.54, Fasc. 1, 1997

Leonel, J.L. and Ramos, J.S., “Weighted Kneading Theory of Unidimensional Maps with holesâ€,, 2003

Misiurewicz, M. and Szlenk, W., “Entropy of piecewise monotone mappings.â€, Studia Math, 67, pp. 45-63, 1980.

Milnor, J. and Thurston, W., “On 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., “Hiperbolicidade e Bifurcação de Sistemas Simbólicosâ€, PhD. Thesis, Universidade de Lisboa, available at, 1989




How to Cite

Cabral, J. (2013). Symbolic Dynamics for Real Rational Maps. Asian Journal of Fuzzy and Applied Mathematics, 1(4). Retrieved from