TY - JOUR

T1 - Boundary influence on the entropy of a Lozi-type map

AU - Jonq, Juang

AU - Chang, Yu Chuan

PY - 2010/11/1

Y1 - 2010/11/1

N2 - 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.

AB - 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.

KW - Boundary influence

KW - Dynamics of intersection

KW - Entropy

KW - Lozi-type map

KW - Smale-Horseshoe

UR - http://www.scopus.com/inward/record.url?scp=77955270911&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2010.06.004

DO - 10.1016/j.jmaa.2010.06.004

M3 - Article

AN - SCOPUS:77955270911

VL - 371

SP - 728

EP - 740

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -