## 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)=h_{D}(T)=h_{N}(T)=h_{D}(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 h_{D}(T) and h_{N}(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 language | English |
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Pages (from-to) | 728-740 |

Number of pages | 13 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 371 |

Issue number | 2 |

DOIs | |

State | Published - 1 Nov 2010 |

## Keywords

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