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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