Rational dynamical zeta functions for birational transformations

N. Abarenkova, J.-Ch. Anglès d'Auriac, S. Boukraa, S. Hassani and J.-M. Maillard

Physica A: Statistical Mechanics and its Applications, 1999, vol. 264, issue 1, 264-293

Abstract: We propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value for the topological entropy. Furthermore, the generating function for the Arnold complexity is also conjectured to be a rational expression with integer coefficients with the same singularities as for the dynamical zeta function. This leads, at least in this example, to an equality between the Arnold complexity and the exponential of the topological entropy. We also give a semi-numerical method to effectively compute the Arnold complexity.

Keywords: Rational dynamical zeta functions; Discrete dynamical systems; Birational mappings; Cremona transformations; Arnold complexity; Topological entropy (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:264:y:1999:i:1:p:264-293

DOI: 10.1016/S0378-4371(98)00452-X

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