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Rigorous exponential asymptotics for a nonlinear third order difference equation

Liu, Xing
http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781

Abstract Details

2004, Doctor of Philosophy, Ohio State University, Mathematics.
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+, 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.
Saleh Tanveer (Advisor)
Yuan Lou (Other)
FeiRan Tian (Other)
Mathematics
Exponential small splitting of separatrices; Exponential asymptotics; Volume preserving map

Recommended Citations

Citations

  • Liu, X. (2004). Rigorous exponential asymptotics for a nonlinear third order difference equation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781

    APA Style (7th edition)

  • Liu, Xing. Rigorous exponential asymptotics for a nonlinear third order difference equation. 2004. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781.

    MLA Style (8th edition)

  • Liu, Xing. "Rigorous exponential asymptotics for a nonlinear third order difference equation." Doctoral dissertation, Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=osu1101927781

    Chicago Manual of Style (17th edition)

osu1101927781
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© 2004, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.