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Lyapunov and Morse exponents in flag bundles
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| Author(s): |
Luciana Aparecida Alves
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2010-03-11 |
| Examining board members: |
Luiz Antonio Barrera San Martin;
Ali Tahzibi;
Jairo da Silva Bochi;
Lucas Conque Seco Ferreira;
Paulo Regis Caron Ruffino
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| Advisor: | Luiz Antonio Barrera San Martin |
| Abstract | |
In this thesis, we study the exponential growth of continuous cocycles wich take vector values on the maximal ag bundle. Such cocycles are intimately connected with the classic Lyapunov exponents, and thus the Oseledets's multiplicative ergodic theorem is proved in the context of semi-simple Lie theory. With this, it is established a connection between the Oseledets decomposition and Morse decomposition in ag bundles. In addition, considering a class of gauge transformations in the bundle, we compare the Morse decomposition obtained in each fiber with the finest Morse decomposition, obtained by Braga and San Martin (AU) | |