publication . Article . 2000

Real topological entropy versus metric entropy for birational measure-preserving transformations

d Auriac, J-Ch Angl s; Viallet, C.; Abarenkova, N.; Anglès d’Auriac, J.-Ch.; Boukraa, S.; Maillard, J.-M.;
Open Access English
  • Published: 01 Oct 2000
  • Publisher: HAL CCSD
  • Country: France
Abstract
Abstract We consider a family of birational measure-preserving transformations of two complex variables, depending on one parameter for which simple rational expressions for the dynamical zeta function have been conjectured, together with an equality between the topological entropy and the logarithm of the Arnold complexity (divided by the number of iterations). Similar results have been obtained for the adaptation of these two concepts to dynamical systems of real variables, yielding to introduce a “real topological entropy” and a “real Arnold complexity”. We try to compare, here, the Kolmogorov–Sinai metric entropy and this real Arnold complexity, or real topo...
Subjects
free text keywords: [PHYS]Physics [physics], [MATH]Mathematics [math], Statistical and Nonlinear Physics, Condensed Matter Physics, Logarithm, Chaotic, Expression (mathematics), Division (mathematics), Topological entropy, Dynamical systems theory, Discrete mathematics, Mathematical analysis, Riemann zeta function, symbols.namesake, symbols, Lyapunov function, Mathematics
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