Absolute Continuity of Stable Foliations for Mappings of Banach Spaces

Alex Blumenthal, Lai Sang Young

Research output: Research - peer-reviewArticle

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.

LanguageEnglish (US)
Pages591-619
Number of pages29
JournalCommunications in Mathematical Physics
Volume354
Issue number2
DOIs
StatePublished - Sep 1 2017

Fingerprint

Absolute Continuity
Foliation
Banach space
continuity
pulse detonation engines
Ergodicity
Submanifolds
Phase Space
Class

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Communications in Mathematical Physics, Vol. 354, No. 2, 01.09.2017, p. 591-619.

Research output: Research - peer-reviewArticle

@article{0e1ac803408645d9a67be66cb0634ed8,
title = "Absolute Continuity of Stable Foliations for Mappings of Banach Spaces",
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.",
author = "Alex Blumenthal and Young, {Lai Sang}",
year = "2017",
month = "9",
doi = "10.1007/s00220-017-2912-z",
volume = "354",
pages = "591--619",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "2",

}

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 -