On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators
| dc.contributor.author | Sorge, Joshua | |
| dc.contributor.supervisor | Bose, Christopher | |
| dc.date.accessioned | 2008-11-17T23:03:01Z | |
| dc.date.available | 2008-11-17T23:03:01Z | |
| dc.date.copyright | 2008 | en_US |
| dc.date.issued | 2008-11-17T23:03:01Z | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/1257 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | Frobenius-Perron operator | en_US |
| dc.subject | Koopman operator | en_US |
| dc.subject | cyclic | en_US |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering::Mathematics | en_US |
| dc.title | On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators | en_US |
| dc.type | Thesis | en_US |