The Multiplicative Ergodic Theorem is a powerful tool for studying certain types of dynamical systems, involving real matrix cocycles. It gives a block diagonalization of these cocycles, according to the Lyapunov exponents. We ask if it is always possible to refine the diagonalization to a block upper-triangularization, and if not over the real numbers, then over the complex numbers. After building up to the posing of the question, we prove that there are counterexamples to this statement, and give concrete examples of matrix cocycles which cannot be block upper-triangularized. / Graduate / 0405 / jahoran@uvic.ca
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/5970 |
| Date | 14 April 2015 |
| Creators | Horan, Joseph Anthony |
| Contributors | Quas, Anthony Nicholas, Bose, Christopher J. |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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