Local rigidity of homogeneous parabolic actions: I. A model case

Danijela Damjanovic, Anatole Katok

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We show a weak form of local differentiable rigidity for the rank 2 abelian action of upper unipotents on SL(2,R) × SL(2,R) Γ. Namely, for a 2- parameter family of sufficiently small perturbations of the action, satisfying certain transversality conditions, there exists a parameter for which the perturbation is smoothly conjugate to the action up to an automorphism of the acting group. This weak form of rigidity for the parabolic action in question is optimal since the action lives in a family of dynamically different actions. The method of proof is based on a KAM-type iteration and we discuss in the paper several other potential applications of our approach.

Original languageEnglish (US)
Pages (from-to)203-235
Number of pages33
JournalJournal of Modern Dynamics
Volume5
Issue number2
DOIs
StatePublished - Apr 1 2011

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Rigidity
Model
Transversality Condition
Small Perturbations
Automorphism
Differentiable
Perturbation
Iteration
Family
Form

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Cite this

Damjanovic, Danijela ; Katok, Anatole. / Local rigidity of homogeneous parabolic actions : I. A model case. In: Journal of Modern Dynamics. 2011 ; Vol. 5, No. 2. pp. 203-235.
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Local rigidity of homogeneous parabolic actions : I. A model case. / Damjanovic, Danijela; Katok, Anatole.

In: Journal of Modern Dynamics, Vol. 5, No. 2, 01.04.2011, p. 203-235.

Research output: Contribution to journalArticle

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