Equations cohomologiques de flots riemanniens et de diffeomorphismes d'Anosov
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概要
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In this paper: i) We compute the leafwise cohomology of a complete Riemannian Diophantine flow. ii) We solve explicitly the discrete cohomological equation for the Anosov diffeomorphism on the torus <B><I>T</I></B><I><SUP>n</SUP></I> defined by a hyperbolic and diagonalizable matrix <I>A</I>∈<I>SL</I>(<I>n</I>,<B><I>Z</I></B>) whose eigenvalues are all real positive numbers. We use this to solve the continuous cohomological equation of the Anosov flow \\mathcal{F} on the hyperbolic torus <B><I>T</I></B><I><SUB>A</SUB></I><SUP><I>n</I>+1</SUP> obtained from <I>A</I> by suspension. This enables us to compute some other geometrical objects associated to the diffeomorphism <I>A</I> and the foliation \\mathcal{F} like the invariant distributions and the leafwise cohomology.
- Mathematical Society of Japanの論文
- 2007-10-01
著者
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El Kacimi
Lamav Le Mont Houy Universite De Valenciennes
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Dehghan-nezhad Akbar
Lamav Le Mont Houy Universite De Valenciennes