Boundary influence on the entropy of a Lozi-type map

Juang Jonq*, Yu Chuan Chang

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let T be a Henon-type map induced from a spatial discretization of a reaction-diffusion system. With the above-mentioned description of T, the following open problems were raised in [V.S. Afraimovich, S.B. Hsu, Lectures on Chaotic Dynamical Systems, AMS International Press, 2003]. Is it true that, in general, h(T)=hD(T)=hN(T)=hD(1),=(2)(T)= Here h(T) and h=(1),=(2)(T) (see Definitions 1.1 and 1.2) are, respectively, the spatial entropy of the system T and the spatial entropy of T with respect to the lines =(1) and =(2), and hD(T) and hN(T) are spatial entropy with respect to the Dirichlet and Neuman boundary conditions. If it is not true, then which parameters of the lines =(i), i=1,2, are responsible for the value of h(T)= What kind of bifurcations occurs if the lines =(i) move= In this paper, we show that this is in general not always true. Among other things, we further give conditions for which the above problem holds true.

Original languageEnglish
Pages (from-to)728-740
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume371
Issue number2
DOIs
StatePublished - 1 Nov 2010

Keywords

  • Boundary influence
  • Dynamics of intersection
  • Entropy
  • Lozi-type map
  • Smale-Horseshoe

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