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Local rigidity of higher rank non-abelian action on torus

Published online by Cambridge University Press:  25 September 2017

ZHENQI JENNY WANG
ZHENQI JENNY WANG*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA email [email protected]
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Abstract

In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms. In former papers all examples for actions enjoying the local smooth rigidity phenomenon are higher rank and have no rank-one factors. In this paper we give examples of smooth rigidity of actions having rank-one factors. The method is a generalization of the KAM (Kolmogorov–Arnold–Moser) iterative scheme.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 6 , June 2019 , pp. 1668 - 1709
Copyright
© Cambridge University Press, 2017 

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