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Electronic Research Announcements in Mathematical Sciences (ERA-MS)
 

Special functions created by Borel-Laplace transform of Hénon map

Pages: 1 - 11, January 2011      doi:10.3934/era.2011.18.1

 
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Chihiro Matsuoka - Department of Physics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan (email)
Koichi Hiraide - Department of Mathematics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan (email)

Abstract: We present a novel class of functions that can describe the stable and unstable manifolds of the Hénon map. We propose an algorithm to construct these functions by using the Borel-Laplace transform. Neither linearization nor perturbation is applied in the construction, and the obtained functions are exact solutions of the Hénon map. We also show that it is possible to depict the chaotic attractor of the map by using one of these functions without explicitly using the properties of the attractor.

Keywords:  Borel-Laplace transform, asymptotic expansion, difference equation, Hénon map.
Mathematics Subject Classification:  Primary: 39A45; Secondary: 44A10.

Received: June 2010;      Available Online: January 2011.

 References