Lozi mappings and symbolic dynamics.

Abstract: In 1978 Lozi introduced a two-parameter family of piecewise linear homeomorphisms of the plane which may give rise to very complicated chaotic dynamics and strange attractors. In 1997 Ishii coded the Lozi strange attractors by bi-infinite sequences of two symbols, which are called itineraries (of points of attractor). He proved that the Lozi map restricted to its strange attractor is topologically conjugate to the shift homeomorphism restricted to the corresponding symbol space, the space of all itineraries. I will show necessary and sufficient conditions that a bi-infinite sequence of two symbols be an itinerary of a point of the Lozi attractor, and discuss some interesting questions which arise from that result.