Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic ℝk actions

Danijela Damjanović, Anatoly Katok

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on SL(n,ℝ)/Γ and SL(n,ℂ)/Γ for n ≥ 3 and Γ cocompact lattice, and for restrictions of those actions to subspaces which contain a two-dimensional plane in general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of generating relations in the group SLn.

Original languageEnglish (US)
Pages (from-to)985-1005
Number of pages21
JournalDiscrete and Continuous Dynamical Systems
Volume13
Issue number4
StatePublished - Nov 1 2005

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Harmonic analysis
Cocycle
Rigidity
Cycle
Harmonic Analysis
Foliation
Unstable
Subspace
Restriction

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic ℝk actions. / Damjanović, Danijela; Katok, Anatoly.

In: Discrete and Continuous Dynamical Systems, Vol. 13, No. 4, 01.11.2005, p. 985-1005.

Research output: Contribution to journalArticle

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