On Brouwer’s Homeomorphisms in Plane

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Shahi, Alireza | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40377 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fanayi, Hamid Reza
Abstract:
In this project we investigate Brouwer’s homeomorphisms in the plane. A Brouwer’s homeomorphisms is an orientation-preserving and fixed-point-free homeomorphism in the plane. For this purpose we prove Brouwer and scoenflies Theorem in the plane. we prove that bounded connected sets in the Plane that are open or closed and meets an infinite number of it’s iterates under Brouwer homeomorphisms must meets all of them.
Keywords:
Dynamical Systems ; Conjugacy Class ; Brouwer Homomorphism ; Brouwer Lemma ; Schoenflies Theorm

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