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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
| Title: | 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. |
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| Name(s): |
Dhakal, Bishal , author Mireles-James, Jason , Thesis advisor Florida Atlantic University, Degree grantor Department of Mathematical Sciences Charles E. Schmidt College of Science |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2023 | |
| Date Issued: | 2023 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 143 p. | |
| Language(s): | English | |
| Abstract/Description: | 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. | |
| Identifier: | FA00014264 (IID) | |
| Degree granted: | Dissertation (PhD)--Florida Atlantic University, 2023. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Manifolds (Mathematics) Morse theory Combinatorial analysis |
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| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00014264 | |
| Use and Reproduction: | Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Host Institution: | FAU |
