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Doctoral Thesis
DOI
Document
Author
Full name
Bruno de Paula Jacóia
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Zanata, Salvador Addas (President)
Boyland, Philip Lewis
Carvalho, André Salles de
Robles, Alejandro Miguel Passeggi Diaz
Tal, Fabio Armando
Title in English
Dynamics of homeomorphisms on surfaces of genus greater than one
Keywords in English
Rotation sets
Surface dynamics
Abstract in English
We consider closed orientable surfaces S of genus greater than one and homeomorphisms f homotopic to the identity. A set of hypotheses is presented, called fully essential system of curves, and it is shown that under these hypotheses, the natural lift of f to the universal cover of S (the Poincaré disk), has complicated and rich dynamics. We also show that the homological rotation set of such a f is a compact convex set with maximal dimension and all points in its interior are realized by compact f-invariant sets, periodic orbits in the rational case.
Title in Portuguese
Dinâmica de homeomorfismos em superfícies de gênero maior do que um
Keywords in Portuguese
Conjuntos de rotação
Dinâmica em superfícies
Abstract in Portuguese
Consideramos superfícies fechadas orientáveis S de gênero maior do que um e homeomorfismos f homotópicos a identidade. Apresentamos um conjunto de hipóteses, chamado sistema de curvas totalmente essencial, e mostramos que sob essas hipóteses, o levantamento natural de f para o recobrimento universal de S (o disco de Poincaré), tem uma dinâmica rica e complicada. Mostramos também que o conjunto de rotação homológico de f é um subconjunto compacto convexo de dimensão máxima e todos os pontos no seu interior são realizados por conjuntos compactos f-invariantes, órbitas periódicas no caso racional.
 
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TeseBrunoJacoia.pdf (968.55 Kbytes)
Publishing Date
2019-04-24
 
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