標題: Boundary influence on the entropy of a Lozi-type map
作者: Juang, Jonq
Chang, Yu-Chuan
應用數學系
數學建模與科學計算所(含中心)
Department of Applied Mathematics
Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
關鍵字: Boundary influence;Lozi-type map;Dynamics of intersection;Entropy;Smale-Horseshoe
公開日期: 15-十一月-2010
摘要: 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) = hl((1)),(l(2)) (T)? Here h(T) and hl((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 e(l) and E(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 l((1)), i = 1.2, are responsible for the value of h(T)? What kind of bifurcations occurs if the lines l((1)) 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. (C) 2010 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jmaa.2010.06.004
http://hdl.handle.net/11536/31935
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.06.004
期刊: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume: 371
Issue: 2
起始頁: 728
結束頁: 740
顯示於類別:期刊論文


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