標題: | Chaotic orbits for differentiable maps near anti-integrable limits |
作者: | Chen, Te-Hsuan Lin, Wen-Wei Peng, Chen-Chang 應用數學系 Department of Applied Mathematics |
關鍵字: | Anti-integrable limits;Snap-back repellers;Heteroclinical repellers;Transversal homoclinic orbits;Henon maps;The Arneodo-Coullet-Tresser maps |
公開日期: | 1-三月-2016 |
摘要: | In this work, we study the dynamical system which can be transformed into a difference equation of the form epsilon g(x(t-n2),...,x(t),..,x(t+n1) ;epsilon) + go (x(t)) = 0 where epsilon is an element of R is a parameter, g : Rn1+n2+1 -> R and go : R -> R. are both C-1 functions and n(1), n(2) are both nonnegative integers. Suppose that the function go has k simple zeros where k >= 2. We give criteria of existence of some kinds of chaotic orbits, and construct infinite ones explicitly. As applications of these results, we establish snap-back repellers and heteroclinical repellers for the modified Mira maps and transversal homoclinic orbits or transversal heteroclinic orbits for the Henon maps, the Arneodo-Coullet-Tresser maps and the quadratic volume preserving maps. (C) 2015 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jmaa.2015.10.058 http://hdl.handle.net/11536/129323 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2015.10.058 |
期刊: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Volume: | 435 |
起始頁: | 889 |
結束頁: | 916 |
顯示於類別: | 期刊論文 |