TY - JOUR
AU - Barreira, Luis
AU - Valls, Claudia
PY - 2011/06/30
Y2 - 2023/01/28
TI - Center Manifolds Optimal Regularity for Nonuniformly Hyperbolic Dynamics
JF - São Paulo Journal of Mathematical Sciences
JA - São Paulo J. Math. Sci.
VL - 5
IS - 1
SE -
DO - 10.11606/issn.2316-9028.v5i1p1-22
UR - https://www.revistas.usp.br/spjournal/article/view/65
SP - 1-22
AB - <span style="font-family: CMR9; font-size: xx-small;"><span style="font-family: CMR9; font-size: xx-small;"><p>For suciently small perturbations with continuous derivative, we show how to establish the optimal regularity of invariant center manifolds when the linear equation admits a nonuniform exponential trichotomy. We also consider the general case of exponential growth rates given by an arbitrary function. This includes the usual exponential behavior as a very special case. Our proof uses the ber contraction principle to establish the regularity property. We note that the argument also applies to sufficiently small linear perturbations, without further changes.</p></span></span>
ER -