Some invariants for σ-permutation maps
Abstract
In this paper we obtain some formulas which allow us to compute topological and metric entropy and topological pressure for a new class of maps. It is also shown that similar formulas do not hold for metric and topological sequence entropy and a new commutativity problem is posed.
References
1. F. Balibrea, J.S. Cánovas Peña, V. Jiménez López, Some results on entropy and sequence entropy, Internat. J. Bifur. Chaos Appl. Sci. Engrg. (to appear).
2. F. Balibrea, J.S. Cánovas Peña, V. Jiménez López, Commutativity and non-commutativity of the topological sequence entropy, Ann. Inst. Fourier (to appear).
3. F. Balibrea, A. Linero, On the periodic structure of the σ-permutation maps on the unit square, this issue, 39-49.
4. R.A. Dana, L. Montrucchio, Dynamic complexity in duopoly games, Journal of Economic Theory 44 (1986), 40-56.
5. T.N.T. Goodman, Topological sequence entropy, Proc. London Math. Soc. 29 (1974), 331-350.
6. S. Kolyada, L. Snoha, Topological entropy of nonautonomous dynamical systems, Random and Comp. Dynamics 4 (1996), 205-233.
7. A.G. Kushnirenko, On metric invariants of entropy type, Russian Math. Surveys 22 (1967), 53-61.
8. A. Linero, Cuestiones sobre dinámica topológica de algunos sistemas bidimensionales y medidas invariantes de sistemas unidimensionales asociados, PhD Thesis, Universidad de Murcia, 1998.
9. P. Walters, An introduction to ergodic theory, Springer Verlag, Berlin 1982.
2. F. Balibrea, J.S. Cánovas Peña, V. Jiménez López, Commutativity and non-commutativity of the topological sequence entropy, Ann. Inst. Fourier (to appear).
3. F. Balibrea, A. Linero, On the periodic structure of the σ-permutation maps on the unit square, this issue, 39-49.
4. R.A. Dana, L. Montrucchio, Dynamic complexity in duopoly games, Journal of Economic Theory 44 (1986), 40-56.
5. T.N.T. Goodman, Topological sequence entropy, Proc. London Math. Soc. 29 (1974), 331-350.
6. S. Kolyada, L. Snoha, Topological entropy of nonautonomous dynamical systems, Random and Comp. Dynamics 4 (1996), 205-233.
7. A.G. Kushnirenko, On metric invariants of entropy type, Russian Math. Surveys 22 (1967), 53-61.
8. A. Linero, Cuestiones sobre dinámica topológica de algunos sistemas bidimensionales y medidas invariantes de sistemas unidimensionales asociados, PhD Thesis, Universidad de Murcia, 1998.
9. P. Walters, An introduction to ergodic theory, Springer Verlag, Berlin 1982.
BalibreaF., Cánovas PeñaJ. S., & LópezV. J. (1999). Some invariants for σ-permutation maps. Annales Mathematicae Silesianae, 13, 51-60. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14136
Francisco Balibrea
balibrea@fcu.um.es
Departamento de Matemáticas, Universidad de Murcia, Spain Spain
Departamento de Matemáticas, Universidad de Murcia, Spain Spain
Jose S. Cánovas Peña
Departamento de Matemáticas Aplicada, Universidad Politécnica de Cartagena, Spain Spain
Departamento de Matemáticas Aplicada, Universidad Politécnica de Cartagena, Spain Spain
Víctor Jiménez López
Departamento de Matemáticas, Universidad de Murcia, Spain Spain
Departamento de Matemáticas, Universidad de Murcia, Spain Spain
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
