Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator

Details Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator

2010-06-09

arxiv.org/abs/1006.1928v1

Mathematics

Dynamical Systems

21 pages

Scientific paper

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom($F$), of non-compact 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.

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