Topological entropy and Arnold complexity for two-dimensional mappings |
| |
| Affiliation: | 1. Centre de Recherches sur les Très Basses Températures, B.P. 166, F-38042 Grenoble, France;2. Theoretical Physics Department, Sankt Petersburg State University, Ulyanovskaya 1, 198904 Sankt Petersburg, Russia;3. Institut d''Aéronautique, Université de Blida, BP 270, Blida, Algeria;4. CDTN, Boulevard F.Fanon, 16000 Alger, Algeria;5. LPTHE, Tour 16, 1er étage, 4 Place Jussieu, 75252 Paris Cedex, France;1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia;2. University of Lincoln, UK;3. Department of Mathematics, University of Brasilia, DF 70910-900, Brazil;1. Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ, 21945-970, Brazil;3. Department of Mathematics, University of Louisville, Louisville, KY 40292, USA;4. Department of Mathematics, Ashoka University, Rajiv Gandhi Education City Kundli, Rai 131029, India;5. Departamento de Matemática, Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, Jardim Nazareth, São José do Rio Preto, SP, 15054-000, Brazil;6. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil;1. School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK;2. Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway |
| |
| Abstract: | To test a possible relation between topological entropy and Arnold complexity, and to provide a nontrivial examples of rational dynamical zeta functions, we introduce a two-parameter family of discrete birational mappings of two complex variables. We conjecture rational expressions with integer coefficients for the number of fixed points and degree generating functions. We then deduce equal algebraic values for the complexity growth and for the exponential of the topological entropy. We also explain a semi-numerical method which supports these conjectures and localizes the integrable cases. We briefly discuss the adaptation of these results to the analysis of the same birational mapping seen as a mapping of two real variables. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
