Absolute Continuity of Stable Foliations for Mappings of Banach Spaces

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 pha...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2017-09, Vol.354 (2), p.591-619
Main Authors: Blumenthal, Alex, Young, Lai-Sang
Format: Article
Language:English
Subjects:
Banach spaces
Classical and Quantum Gravitation
Complex Systems
Continuity
Dimensional stability
Dissipation
Ergodic processes
Error analysis
Manifolds (mathematics)
Mathematical analysis
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-017-2912-z