Homeomorphisms group of normed vector spaces : The conjugacy problem and the Koopman operator

Citation:

Chekroun, M. D., and J. Roux. 2013. “Homeomorphisms group of normed vector spaces : The conjugacy problem and the Koopman operator.” Discrete and Continuous Dynamical Systems (DCDS-A) 33 (9): 3957—3950.

Abstract:

This article is concerned with conjugacy problems arising in the homeomorphisms group, Hom(F), of unbounded subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on Hom(F), where the conjugacy is obtained as limit of a sequence generated by the conjugacy operator, when this limit exists. The main conjugacy theorem is presented in a class of generalized Lipeomorphisms.

Publisher's Version

Last updated on 04/19/2020