Mixing for Finite Systems of Coupled Tent Maps

It is shown that a finite system of coupled mixing tent maps has a unique absolutely continuous invariant measure and is exact with respect to this measure provided the coupling strength does not exceed a certain value ffl uni which is independent of the size of the system. 1 Introduction and main result Systems of coupled maps were widely studied during the last years, mostly by physicists, see [10, 5] for reviews. On the mathematical side two approaches to their understanding emerged: Initiated by Bunimovich and Sinai [3] several authors constructed models of statistical mechanics equivalent to infinite systems of coupled maps and studied invariant measures in this setting. Recent expositions of this type of approach are given in [2, 1]. On the other hand the dynamics of coupled maps were analyzed in terms of the transfer operator [8, 9], see also [7] for a brief review. In this note we continue this line of research. More specifically, we study finite systems of coupled tent maps ..