Special functions created by Borel-Laplace transform of Hénon map

Chihiro Matsuoka; Koichi Hiraide

doi:10.3934/era.2011.18.1

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2011, Volume 18: 1-11. Doi: 10.3934/era.2011.18.1

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Special functions created by Borel-Laplace transform of Hénon map

Chihiro Matsuoka^1, and
Koichi Hiraide^2,

1.
Department of Physics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577
2.
Department of Mathematics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577

Received: May 31, 2010

Published: December 2010

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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.

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Mathematics Subject Classification: Primary: 39A45; Secondary: 44A10.

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References

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