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Absolute Continuity of Stable Foliations for Mappings of Banach Spaces

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Abstract

We prove the absolute continuity of stable foliations for mappings of Banach spaces satisfying conditions consistent with time-t maps of certain classes of dissipative PDEs. This property is crucial for passing information from submanifolds transversal to the stable foliation to the rest of the phase space; it is also used in proofs of ergodicity. Absolute continuity of stable foliations is well known in finite dimensional hyperbolic theory. On Banach spaces, the absence of nice geometric properties poses some additional difficulties.

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Correspondence to Lai-Sang Young.

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Communicated by C. Liverani

Lai-Sang Young was supported in part by NSF grant DMS-1363161. This work was done while Alex Blumenthal was a doctoral student at the Courant Institute of Mathematical Sciences, New York University.

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Blumenthal, A., Young, LS. Absolute Continuity of Stable Foliations for Mappings of Banach Spaces. Commun. Math. Phys. 354, 591–619 (2017). https://doi.org/10.1007/s00220-017-2912-z

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  • DOI: https://doi.org/10.1007/s00220-017-2912-z

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