Tsang, Chi Shing Sidney. / "October 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 58-59). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The main results --- p.6 / Chapter 1.2 --- Structure of the thesis --- p.8 / Chapter 2 --- The Upper Lyapunov Exponent --- p.10 / Chapter 2.1 --- Notation --- p.10 / Chapter 2.2 --- The upper Lyapunov exponent --- p.11 / Chapter 2.3 --- Cocycles --- p.12 / Chapter 2.4 --- The Theorem of Furstenberg and Kesten --- p.14 / Chapter 3 --- Contraction Properties --- p.19 / Chapter 3.1 --- Two basic lemmas --- p.20 / Chapter 3.2 --- Contracting sets --- p.25 / Chapter 3.3 --- Strong irreducibility --- p.29 / Chapter 3.4 --- A key property --- p.30 / Chapter 3.5 --- Contracting action on P(Rd) and converges in direction --- p.36 / Chapter 3.6 --- Lyapunov exponents --- p.39 / Chapter 3.7 --- Comparison of the top Lyapunov exponents and Fursten- berg's theorem --- p.43 / Chapter 4 --- Analytic Dependence of Lyapunov Exponents on The Probabilities --- p.48 / Chapter 4.1 --- Continuity and analyticity properties for i.i.d. products --- p.49 / Chapter 4.2 --- The proof of the main result --- p.50 / Chapter 5 --- The Expression of The Upper Lyapunov Exponent in Complex Functions --- p.54 / Chapter 5.1 --- The set-up --- p.54 / Chapter 5.2 --- The main result --- p.56 / Bibliography --- p.58
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327161 |
| Date | January 2010 |
| Contributors | Tsang, Chi Shing Sidney., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 1, 59 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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