Geodesic
Nonstationary normal forms and rigidity of group actions
Katok, A.1 ; Spatzier, R.2
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48103
Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 3, pp. 124-133.

Voir la notice de l'article provenant de la source American Mathematical Society

We develop a proper “nonstationary” generalization of the classical theory of normal forms for local contractions. In particular, it is shown under some assumptions that the centralizer of a contraction in an extension is a particular Lie group, determined by the spectrum of the linear part of the contractions. 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 actions of cocompact lattices on Furstenberg boundaries, in particular projective spaces, and (ii) the actions by automorphisms of tori and nilmanifolds. The main new technical ingredient in the proofs is the centralizer result mentioned above.
DOI : 10.1090/S1079-6762-96-00016-9

Katok, A. 1 ; Spatzier, R. 2

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48103 
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Katok, A.; Spatzier, R. Nonstationary normal forms and rigidity of group actions. Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 3, pp. 124-133. doi : 10.1090/S1079-6762-96-00016-9. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-96-00016-9/

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