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Master's Dissertation
DOI
10.11606/D.55.2006.tde-28082006-151440
Document
Author
Full name
Walter Teofilo Huaraca Vargas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2006
Supervisor
Committee
Apaza, Carlos Alberto Maquera (President)
Firmo, Sebastião Marcos Antunes
Vidalon, Carlos Teobaldo Gutierrez
Title in Portuguese
"Sobre a existência de pontos periódicos para homeomorfismos do anel fechado"
Keywords in Portuguese
anel
homeomorfismos
pontos fixos
Abstract in Portuguese
O conhecido Teorema de Poincaré afirma: O número de rotação de homeomorfismo do círculo S^1 que preserva orientação é racional se, e somente se, o homeomorfismo possui um ponto periódico cujo período é igual ao denominador de tal racional. Na presente dissertação estudamos resultados análogos, ao resultado acima mencionado, para homeomorfismos do anel A=S^1 x I homotópicos à identidade. Mais precisamente, estudaremos o famoso Teorema de Poincaré - Birkhoff e algumas versões devidas a J. Franks. Isto será feito impondo algumas condições no conjunto de rotação, o qual é uma generalização do número de rotação para homeomorfismos do círculo.
Title in English
"On the existence of periodic points for homeomorphisms of the closed annulus"
Keywords in English
annulus
fixed points
homeomorphisms
Abstract in English
The well known Poincaré's Theorem state: The rotation number of an orientation preserving circle homeomorphism is rational if, only if, the homeomorphism has a periodic point of period equal to denominator of the rational. In this monograph we study results analogous, to the result above mentioned, for homeomorphisms of A=S^1 x I homotophics to the identity. More precisely, we study the famous Poincaré - Birkhoff Theorem and some versions obtained by J. Franks. This it will be done imposing some conditions in the rotation set, which is generalization of the rotation number for circle homeomorphisms.
 
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disertacioncpg.pdf (315.16 Kbytes)
Publishing Date
2006-09-11
 
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