Approximation scheme of a center manifold for functional-differential equations. Ait Babram, M., Hbid, M. L., & Arino, O. J. Math. Anal. Appl., 213(2):554–572, 1997. abstract bibtex Consider the autonomous functional-differential equation $(*) \ dx/dt = Lx_t + f(x_t)$ where $L$ is a bounded linear operator, $f$ is sufficiently smooth and satisfies $f(0)=0$, $f'(0)=0$. Assuming that $(*)$ has a center manifold, the authors derive an algorithm to compute the terms in the Taylor expansion of this manifold up to any order.
@Article{AitBabramHbidArino1997,
author = {Ait Babram, M. and Hbid, M. L. and Arino, Ovide},
title = {Approximation scheme of a center manifold for functional-differential equations},
journal = {J. Math. Anal. Appl.},
year = {1997},
volume = {213},
number = {2},
pages = {554--572},
issn = {0022-247X},
abstract = {Consider the autonomous functional-differential
equation $(*) \ dx/dt = Lx_t + f(x_t)$ where $L$ is
a bounded linear operator, $f$ is sufficiently
smooth and satisfies $f(0)=0$, $f'(0)=0$. Assuming
that $(*)$ has a center manifold, the authors derive
an algorithm to compute the terms in the Taylor
expansion of this manifold up to any order.},
coden = {JMANAK},
fjournal = {Journal of Mathematical Analysis and Applications},
keywords = {autonomous functional-differential equation; center manifold; Taylor expansion},
mrclass = {34K15 (34A45 34C20 34C40)},
mrnumber = {98h:34122},
mrreviewer = {Teresa Faria},
pdf = {AitbabramHbidArino-1997-JMAA213.pdf},
source = {J. Math. Anal. Appl. 213, No.2, 554-572 (1997). [ISSN 0022-247X] http://www.europe.idealibrary.com/},
}
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