https://doi.org/10.1140/epjst/e2014-02309-5
Regular Article
A rational transformation conjugated to the Arnold-Thom Cat map
An application of the Schröder method to hyperbolic toral maps
Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, CP 02200, México, DF, México
a e-mail: jrle@correo.azc.uam.mx
Received: 11 August 2014
Revised: 17 October 2014
Published online: 10 December 2014
We compute a vector-valued rational map conjugated to the Arnold-Thom Cat map by means of Schröder's method. The corresponding invariant density and the spectrum of Rényi information are analytically determined. We show that for the analogous n-dimensional case the invariant density is the product of n Cauchy densities. Hence, the spectrum of Rényi information is n times the corresponding Rényi information of a Cauchy density. We also work out two three-dimensional linear toral maps as an example of the general case.
© EDP Sciences, Springer-Verlag, 2014
