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

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  • 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.
    Mathematics Subject Classification: 20E45, 37C15, 39B62, 39B72, 47A75, 47B33, 54A20, 54E15, 54E25, 57S05.


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