TY - JOUR
T1 - Absolute continuity of stable foliations for systems on Banach spaces
AU - Lian, Zeng
AU - Young, Lai Sang
AU - Zeng, Chongchun
N1 - Funding Information:
E-mail addresses: [email protected] (Z. Lian), [email protected] (L.-S. Young), [email protected] (C. Zeng). 1 This research was supported in part by NSF Grant DMS-1101594. 2 This research was supported in part by NSF Grant DMS-0801319.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - We prove the absolute continuity of stable foliations for C 1,α maps of Banach spaces satisfying a globally defined infinitesimal invariant cones condition. Proofs of regularity for center and stable manifolds needed for the main theorem are included. Our results are applicable to dynamical systems generated by ordinary, partial, or functional differential equations, including non-autonomous differential equations that are periodic in time.
AB - We prove the absolute continuity of stable foliations for C 1,α maps of Banach spaces satisfying a globally defined infinitesimal invariant cones condition. Proofs of regularity for center and stable manifolds needed for the main theorem are included. Our results are applicable to dynamical systems generated by ordinary, partial, or functional differential equations, including non-autonomous differential equations that are periodic in time.
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U2 - 10.1016/j.jde.2012.08.021
DO - 10.1016/j.jde.2012.08.021
M3 - Article
AN - SCOPUS:84867634037
SN - 0022-0396
VL - 254
SP - 283
EP - 308
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -