### 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.

Language | English (US) |
---|---|

Pages | 591-619 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 354 |

Issue number | 2 |

DOIs | |

State | Published - Sep 1 2017 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*354*(2), 591-619. DOI: 10.1007/s00220-017-2912-z

**Absolute Continuity of Stable Foliations for Mappings of Banach Spaces.** / Blumenthal, Alex; Young, Lai Sang.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol 354, no. 2, pp. 591-619. DOI: 10.1007/s00220-017-2912-z

}

TY - JOUR

T1 - Absolute Continuity of Stable Foliations for Mappings of Banach Spaces

AU - Blumenthal,Alex

AU - Young,Lai Sang

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85020082701&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020082701&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-2912-z

DO - 10.1007/s00220-017-2912-z

M3 - Article

VL - 354

SP - 591

EP - 619

JO - Communications in Mathematical Physics

T2 - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -