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Attractive invariant manifolds for maps: Existence, smoothness and continuous dependence on the map

by K. Nipp and D. Stoffer

(Report number 1992-11)

Abstract
A global invariant manifold result for maps is derived with conditions that are easy to verify for applications. The result supplies existence and smoothness of the attractive manifold as well as additional useful properties. It is also shown that a Ck,1-perturbation of the map yields a Ck-perturbation of the manifold. Moreover, it is proved that if there is an attractive invariant manifold for the time-T map of an ODE then this manifold is invariant for the flow as well. For an illustration, the results are applied to a system of two weakly coupled harmonic oscillators.

Keywords: attractive invariant manifold, centre-unstable manifold, smooth manifold

@Techreport{NS92_21,
  author = {K. Nipp and D. Stoffer},
  title = {Attractive invariant manifolds for maps: Existence, smoothness and continuous dependence on the map},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-11.pdf },
  year = {1992}
}

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