Rigorous exponential asymptotics for a nonlinear third order difference equation

Rigorous exponential asymptotics for a nonlinear third order difference equation

Bibliographic Details
Main Author: Liu, Xing
Language:English
Published: The Ohio State University / OhioLINK 2004
Subjects:
Mathematics
Exponential small splitting of separatrices
Exponential asymptotics
Volume preserving map
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu11019277812021-08-03T05:49:29Z Rigorous exponential asymptotics for a nonlinear third order difference equation Liu, Xing Mathematics Exponential small splitting of separatrices Exponential asymptotics Volume preserving map In the present thesis, we study a particular 3-D map with a parameter ε>0, which has two fixed points. One fixed point has a 1-D unstable manifold, while the other has a 1-D stable manifold. The main result is that we prove the smallest distance between theupdate.cgi two manifolds is exponentially small in ε for small ε. We first prove in the limit of ε → 0<sup>+</sup>, bounded away from +∞ or -∞, both the stable and unstable manifolds asymptotes to a heteroclinic orbit for a differential equation. Then we show there exists a parameterization of the manifolds so that they differ exponentially in ε. By examining the inner region around the nearest complex singularity of the limiting solution, and using Borel analysis, we relate the constant multiplying the exponentially small term to the Stokes constant of the leading order inner equation. 2004 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781 http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Exponential small splitting of separatrices
Exponential asymptotics
Volume preserving map
spellingShingle Mathematics
Exponential small splitting of separatrices
Exponential asymptotics
Volume preserving map
Liu, Xing
Rigorous exponential asymptotics for a nonlinear third order difference equation
author Liu, Xing
author_facet Liu, Xing
author_sort Liu, Xing
title Rigorous exponential asymptotics for a nonlinear third order difference equation
title_short Rigorous exponential asymptotics for a nonlinear third order difference equation
title_full Rigorous exponential asymptotics for a nonlinear third order difference equation
title_fullStr Rigorous exponential asymptotics for a nonlinear third order difference equation
title_full_unstemmed Rigorous exponential asymptotics for a nonlinear third order difference equation
title_sort rigorous exponential asymptotics for a nonlinear third order difference equation
publisher The Ohio State University / OhioLINK
publishDate 2004
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781
work_keys_str_mv AT liuxing rigorousexponentialasymptoticsforanonlinearthirdorderdifferenceequation
_version_ 1719426126596538368

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