Real Arnold complexity versus real topological entropy for a one-parameter-dependent two-dimensional birational transformation

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

Physica A: Statistical Mechanics and its Applications, 2000, vol. 281, issue 1, 151-172

Abstract: We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been conjectured. Moreover, an equality between the (asymptotic of the) Arnold complexity and the (exponential of the) topological entropy has been conjectured. This identification takes place for the birational mapping seen as a mapping bearing on two complex variables (acting in a complex projective space). We revisit this identification between these two quite “universal complexities” by considering now the mapping as a mapping bearing on two real variables. The definitions of the two previous “topological” complexities (Arnold complexity and topological entropy) are modified according to this real-variables point of view. Most of the “universality” is lost. However, the results presented here are, again, in agreement with an identification between the (asymptotic of the) “real Arnold complexity” and the (exponential of the) “real topological entropy”. A detailed analysis of the “real Arnold complexity” as a function of the parameter of this family of birational transformations of two variables is given.

Keywords: Arnold complexity; Topological entropy; Discrete dynamical systems of real variables; Birational mappings; Cremona transformations; Rational dynamical zeta functions; Complex mappings (search for similar items in EconPapers)
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100000200
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:281:y:2000:i:1:p:151-172

DOI: 10.1016/S0378-4371(00)00020-0

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().