Accumulation sets and zero entropy dynamics in the Lozi map.

Authors

Kristijan Kilassa Kvaternik

Published in

Chaos (Woodbury, N.Y.). Volume 36. Issue 9. Sep 01, 2026.

Abstract

For the Lozi map La,b, we consider parameter pairs for which the fixed point X has no homoclinic points and the period-two orbit {P, P'} is attracting. For such parameters, let ℓ be the set of accumulation points of the unstable manifold WXu that do not lie on WXu. We construct a polygon D whose forward images under La,b form nested sequences of sets that eventually become trapping. We show that this geometric construction gives a characterization of ℓ as the intersection of these iterates. Using this structure, we prove that the non-wandering set for La,b2 is contained in the union of ℓ and the set of fixed points of La,b. As a consequence, the Lozi map, restricted to the complement of ℓ in the plane, has zero topological entropy. This result extends a recent one of Misiurewicz and Štimac to a broader set of parameters.

PMID:
42720520
Bibliographic data and abstract were imported from PubMed on 10 Sep 2026.

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