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• W2963640830 abstract "We consider a partially hyperbolic $C^1$-diffeomorphism $fcolon Mrightarrow M$ with a uniformly compact $f$-invariant center foliation$mathcal{F}^c$. We show that if the unstable bundle isone-dimensional and oriented, then the holonomy of the centerfoliation vanishes everywhere, the quotient space $M/mathcal{F}^c$ ofthe center foliation is a torus and $f$ induces a hyperbolicautomorphism on it, in particular, $f$ is centrally transitive. We actually obtain further interesting results without restrictions onthe unstable, stable and center dimension: we prove a kind of spectraldecomposition for the chain recurrent set of the quotient dynamics,and we establish the existence of a holonomy-invariant family ofmeasures on the unstable leaves (Margulis measure)." @default.
• W2963640830 created "2019-07-30" @default.
• W2963640830 creator A5042605369 @default.
• W2963640830 date "2013-01-01" @default.
• W2963640830 modified "2023-09-27" @default.
• W2963640830 title "Codimension-1 partially hyperbolic diffeomorphisms with a uniformly compact center foliation" @default.
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• W2963640830 doi "https://doi.org/10.3934/jmd.2013.7.565" @default.
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