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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1997, Volume 216, Pages 292–319 (Mi tm1013)  

This article is cited in 67 scientific papers (total in 67 papers)

Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions

A. Katok, R. J. Spatzier
Abstract: We show that most homogeneous Anosov actions of higher rank Abelian groups are locally $C^\infty$-rigid (up to an automorphism). This result is the main part in the proof of local $C^\infty$-rigidity for two very different types of algebraic actions of irreducible lattices in higher rank semisimple Lie groups: (i) the Anosov actions by automorphisms of tori and nilmanifolds, and (ii) the actions of cocompact lattices on Furstenberg boundaries, in particular, projective spaces. The main new technical ingredient in the proofs is the use of a proper “onstationary” generalization of the classical theory of normal forms for local contractions.
Received in February 1997
Bibliographic databases:
UDC: 517.9
Language: English
Citation: A. Katok, R. J. Spatzier, “Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions”, Dynamical systems and related topics, Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 216, Nauka, Moscow, 1997, 292–319; Proc. Steklov Inst. Math., 216 (1997), 287–314
Citation in format AMSBIB
\Bibitem{KatSpa97}
\by A.~Katok, R.~J.~Spatzier
\paper Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions
\inbook Dynamical systems and related topics
\bookinfo Collection of articles. To the 60th anniversary of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 1997
\vol 216
\pages 292--319
\publ Nauka
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm1013}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1632177}
\zmath{https://zbmath.org/?q=an:0938.37010}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 216
\pages 287--314
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  • This publication is cited in the following 67 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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