Stably Non-Synchronizable Maps of the Plane

Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given n-dimensional dynamical system by imposing the evolution of one coordinate. They noticed that the resulting dynamics may be contracting even if the original dynamics are not. It is easy to construct flows or maps such that no coordinate has synchronizing properties, but this cannot be done in an open set of lineaer maps or flows in Rn, n greater than 2. In this paper we give examples of real analytic maps on R2 such that the synchronizability is stable in the sense that in a full C0 neighborhood of the given map, no map is synchronizable.

By: Patrice Le Calvez (Univ. Paris, France), Marco Martens (SUNY Stony Brook), Charles Tresser and Patrick A. Worfolk (Univ. of MN)

Published in: Nonlinearity, volume 12, (no 1), pages 9-18 in 1999

Please obtain a copy of this paper from your local library. IBM cannot distribute this paper externally.

Questions about this service can be mailed to .