Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors

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10 Citations (Scopus)

Abstract

We construct a kneading theory à la Milnor-Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters.

Original languageEnglish
Pages (from-to)375-394
Number of pages20
JournalCommunications in Mathematical Physics
Volume190
Issue number2
DOIs
Publication statusPublished - Jan 1 1997
Externally publishedYes

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Kneading Theory
Topological Entropy
Pruning
Hausdorff Dimension
Monotonicity
Attractor
entropy
Horseshoe
Upper and Lower Bounds
Bifurcation
analogs
Analogue
Partial
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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