Ergodic Theory and Dynamical Systems

Table of Contents - 01 March 1990 - Volume 10, Issue 01  

Research Article

Monotone recurrence relations, their Birkhoff orbits and topological entropy

Sigurd B. Angenenta1†

a1 University of Wisconsin—Madison Center for the Mathematical Sciences, Wisconsin, USA

Abstract

A generalization of the class of monotone twistmaps to maps of s1 × RN is proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given. These results are then specialized to the case of monotone twist maps. Finally it is shown that there is a large class of symplectic maps to which the foregoing discussion applies.

(Received March 01 1988)

Footnotes

† This research was partially supported by the United States Army under Contract No. DAAL03-87-K-0043, by a NATO Science Fellowship, and by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).