Sorge, Joshua2008-11-172008-11-1720082008-11-17http://hdl.handle.net/1828/1257The 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.enAvailable to the World Wide WebFrobenius-Perron operatorKoopman operatorcyclicUVic Subject Index::Sciences and Engineering::MathematicsThesis