Symbolic dynamics for Lozi maps

We study the family of Lozi maps La,b:R2→R2, La,b(x,y)=(1+y−a|x|,bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches.

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Bibliographic Details
Published in:Nonlinearity 2016-10, Vol.29 (10), p.3031-3046
Main Authors: Misiurewicz, M, Štimac, S
Format: Article
Language:English
Subjects:
kneading theory
Lozi attractor
Lozi map
symbolic dynamics
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Summary:We study the family of Lozi maps La,b:R2→R2, La,b(x,y)=(1+y−a|x|,bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/29/10/3031