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Abbreviated Journal Title

Chaos

Keywords

Stokes Discontinuities; Separatrices; Equation; Growth; Orders; Mathematics; Applied; Physics; Mathematical

Abstract

The subject of this paper is the construction of the exponential asymptotic expansions of the unstable and stable manifolds of the area-preserving Henon map. The approach that is taken enables one to capture the exponentially small effects that result from what is known as the Stokes phenomenon in the analytic theory of equations with irregular singular points. The exponential asymptotic expansions were then used to obtain explicit functional approximations for the stable and unstable manifolds. These approximations are compared with numerical simulations and the agreement is excellent. Several of the main results of the paper have been previously announced in A. Tovbis, M. Tsuchiya, and C. Jaffe ["Chaos-integrability transition in nonlinear dynamical systems: exponential asymptotic approach," Differential Equations and Applications to Biology and to Industry, edited by M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme (World Scientific, Singapore, 1996), pp. 495-507, and A. Tovbis, M. Tsuchiya, and C. Jaffe,"Exponential asymptotic expansions and approximations of the unstable and stable manifolds of the Henon map," preprint, 1994].

Journal Title

Chaos

Volume

8

Issue/Number

3

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

665

Last Page

681

WOS Identifier

WOS:000075898400016

ISSN

1054-1500

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