Absolute Continuity of Stable Foliations for Mappings of Banach Spaces

Alex Blumenthal, Lai Sang Young

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)591-619
Number of pages29
JournalCommunications In Mathematical Physics
Volume354
Issue number2
DOIs
StatePublished - Sep 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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