Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem

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Abstract

We construct a kneading theory à la Milnor-Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). As a two-dimensional analogue of the kneading sequence, the pruning front and the primary pruned region are introduced, and the admissibility criterion for symbol sequences known as the pruning front conjecture is proven under a mild condition on the parameters. Using this result, we show that topological properties of the dynamics of the Lozi mapping are determined by its pruning front and primary pruned region only. This gives us a solution to the first tangency problem for the Lozi family, moreover the boundary of the set of all horseshoes in the parameter space is shown to be algebraic.

Original languageEnglish
Pages (from-to)731-747
Number of pages17
JournalNonlinearity
Volume10
Issue number3
DOIs
Publication statusPublished - May 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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