On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators

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.

Author dc:creator

• Sorge, Joshua

Advisor dc:contributor.supervisor

• Bose, Christopher

• Frobenius-Perron operator
• Koopman operator
• cyclic

Statement dc:rights

• Available to the World Wide Web

Language dc:language.iso

en, English

Handle dc:identifier.uri

http://hdl.handle.net/1828/1257

OAI record oai:identifier

https://dspace.library.uvic.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Adspace.library.uvic.ca%3A1828%2F1257