1998/06/24 by N. Abarenkova, J. -Ch. Anglès d'Auriac, J C Anglès d'Auriac +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Computational Drug Discovery Methods #FOS: Physical sciences #Fractal and DNA sequence analysis #Graph theory and applications #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9806026
1 LaTex file = 4 pages, 2 figures = 2 PostScript files
arxiv created 1998/06/24 · openalex publication_date 1998/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational mappings. The generating functions of the number of fixed points, and of the degree of the successive iterates, are both considered. We conjecture rational expressions with integer coefficients for these two generating functions. and a rational expression for the dynamical zeta function. We then deduce algebraic values for the complexity growth and for the exponential of the topological entropy. Moreover, these two numbers happen to be equal for all the values of the parameters. These conjectures are supported by a semi-numerical method we explain. This method also localizes the integrable cases.