Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Extensive escape rate in lattices of weakly coupled expanding maps

Pages: 669 - 684, Volume 31, Issue 3, November 2011      doi:10.3934/dcds.2011.31.669

       Abstract        References        Full Text (443.7K)       Related Articles       

Jean-Baptiste Bardet - Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS - Université de Rouen, Avenue de l’Université, 76801 Saint Étienne du Rouvray, France (email)
Bastien Fernandez - Centre de Physique Théorique, UMR 6207 CNRS - Université Aix-Marseille II, Campus de Luminy Case 907, 13288 Marseille CEDEX 9, France (email)

Abstract: In this paper, we study the escape rate of infinite lattices of weakly coupled maps with uniformly expanding repeller. In particular, it is proved that the escape rate of spatially periodic approximations is extensive and grows linearly with the period size. The proof relies on symbolic dynamics and is based on the control of cumulative effects of perturbations in cylinder sets with distinct spatial periods. A piecewise affine diffusive example is presented that exhibits monotonic decay of the escape rate with coupling intensity.

Keywords:  Escape Rate, Coupled Map Lattices.
Mathematics Subject Classification:  Primary: 37L60; Secondary: 37D50.

Received: February 2011;      Revised: May 2011;      Available Online: August 2011.