Symbolic Dynamics for Real Rational Maps

Authors

  • João Cabral Azores University

Keywords:

Rational maps, symbolic dynamics, topological entropy, Markov partitions

Abstract

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

References

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€, arxiv.org/abs/math/0302354, 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 http://purl.pt/7368, 1989

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Published

2013-12-13

How to Cite

Cabral, J. (2013). Symbolic Dynamics for Real Rational Maps. Asian Journal of Fuzzy and Applied Mathematics, 1(4). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/597

Issue

Vol. 1 No. 4 (2013): December 2013

Section

Articles

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