Symbolic Dynamics for Real Rational Maps
Keywords:
Rational maps, symbolic dynamics, topological entropy, Markov partitionsAbstract
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.
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
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
