Chaotic Lozi Attractors
by
Chris Cleveland
Rensselaer Polytechnic Institute

The Lozi maps are a two parameter family of planar maps which witness the creation of a topological horseshoe. We show that certain partially formed Lozi horseshoes have a ``chaotic core'' which is contained within a nested family of attractors. This containment restricts the level of dynamical complexity realized on the core. As the horseshoe forms, the core grows, acquiring and destroying the attractors which contain it. The order in which the attractors are acquired by the core is faithful to that dictated by the underlying one dimensional structure of the Lozi maps. This induces a forcing relation on the existence of orbit types in the partially formed Lozi horseshoe, limiting the ways in which the horseshoe itself may form.

Date received: March 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caep-21.