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http://hdl.handle.net/2445/122286
Title: | Punts fixos de difeomorfismes hamiltonians |
Author: | Plandolit López, Bernat |
Director/Tutor: | Mundet i Riera, Ignasi |
Keywords: | Difeomorfismes Treballs de fi de grau Tor (Geometria) Varietats simplèctiques Topologia diferencial Diffeomorphisms Bachelor's theses Torus (Geometry) Symplectic manifolds Differential topology |
Issue Date: | 29-Jun-2017 |
Abstract: | [en] Arnold’s conjecture asserts that every Hamiltonian diffeomorfism of a compact symplectic manifold has at least as many fixed points as a function on the manifold must have critical points. What’s more, if the fixed points are all non degenerate, then the number of fixed points is at least the minimal number of critical points for a Morse function on the manifold. In this project we will give meaning to all the concepts mentioned in the conjecture’s statement and we will study a very specific known result: the case in which the manifolds are 2-dimensional tori and the diffeomorfisms are close enough to identity. We will also generalize some results to 2n-dimensional tori to study the general case for every Hamiltonian diffeomorfism. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Ignasi Mundet i Riera |
URI: | http://hdl.handle.net/2445/122286 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 767.8 kB | Adobe PDF | View/Open |
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