Date of Award
2023
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Mireles-James, Jason
Abstract
The goal of this dissertation is to estimate the precise asymptotics for the number of geometric equivalence classes of Morse functions on the 2-sphere. Our approach involves utilizing the Lagrange inversion formula, Cauchy’s coefficient formula, and the saddle point method for the asymptotic analysis of contour integrals to analyze the generating function derived by L. Nicolaescu, expressed as the inverse of an elliptic integral. We utilize complex analysis, nonlinear functional analysis in infinite sequence spaces, and interval arithmetic to write all the necessary MATLAB programs that validate our results. This work answers questions posed by Arnold and Nicolaescu, furthering our understanding of the topological properties of Morse functions on two-dimensional manifolds. It also demonstrates the effectiveness of a computer assisted approach for asymptotic analysis.
Extent
143 p.
Recommended Citation
Dhakal, Bishal, "SOLVING V.I. ARNOLD’S PROBLEM ABOUT ASYMPTOTIC ENUMERATION OF MORSE FUNCTIONS ON THE 2-SPHERE: A COMBINATORIAL AND ANALYTIC APPROACH WITH COMPUTER ASSISTED PROOFS" (2023). Electronic Theses and Dissertations 2020 - Present. 1285.
https://digitalcommons.fau.edu/etd_general/1285
Identifier
FA00014264
Comments
Includes bibliography.|Dissertation (PhD)--Florida Atlantic University, 2023.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.