An Algorithm to Automatically Detect the Smale Horseshoes
Joint Authors
Yang, Fangyan
Li, Qingdu
Zhang, Lina
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-29
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale's famous example, provide a rigorous way to study chaos in dynamical systems.
The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles.
We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curvilinear rectangle near to segments of the stable and of the unstable manifolds, respectively, and then apply it to four classical chaotic maps (the Duffing map, the Hénon map, the Ikeda map, and the Lozi map) to verify its effectiveness.
American Psychological Association (APA)
Li, Qingdu& Zhang, Lina& Yang, Fangyan. 2012. An Algorithm to Automatically Detect the Smale Horseshoes. Discrete Dynamics in Nature and Society،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-460170
Modern Language Association (MLA)
Li, Qingdu…[et al.]. An Algorithm to Automatically Detect the Smale Horseshoes. Discrete Dynamics in Nature and Society No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-460170
American Medical Association (AMA)
Li, Qingdu& Zhang, Lina& Yang, Fangyan. An Algorithm to Automatically Detect the Smale Horseshoes. Discrete Dynamics in Nature and Society. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-460170
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460170