Invariant manifolds and the concept of asymptotic phase

Bernd Aulbach; Dietrich Flockerzi; Hans-Wilhelm Knobloch

Časopis pro pěstování matematiky (1986)

  • Volume: 111, Issue: 2, page 156-176
  • ISSN: 0528-2195

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Aulbach, Bernd, Flockerzi, Dietrich, and Knobloch, Hans-Wilhelm. "Invariant manifolds and the concept of asymptotic phase." Časopis pro pěstování matematiky 111.2 (1986): 156-176. <http://eudml.org/doc/21640>.

@article{Aulbach1986,
author = {Aulbach, Bernd, Flockerzi, Dietrich, Knobloch, Hans-Wilhelm},
journal = {Časopis pro pěstování matematiky},
keywords = {invariant submanifold; center manifold; invariant manifolds; stable manifold; attractor},
language = {eng},
number = {2},
pages = {156-176},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {Invariant manifolds and the concept of asymptotic phase},
url = {http://eudml.org/doc/21640},
volume = {111},
year = {1986},
}

TY - JOUR
AU - Aulbach, Bernd
AU - Flockerzi, Dietrich
AU - Knobloch, Hans-Wilhelm
TI - Invariant manifolds and the concept of asymptotic phase
JO - Časopis pro pěstování matematiky
PY - 1986
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 111
IS - 2
SP - 156
EP - 176
LA - eng
KW - invariant submanifold; center manifold; invariant manifolds; stable manifold; attractor
UR - http://eudml.org/doc/21640
ER -

References

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  1. B. Aulbach, A reduction principle for nonautonomous differential equations, Arch. Malh. 39 (1982), 217-232. (1982) Zbl0521.34049MR0682449
  2. E. A. Coddington, N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York 1955. (1955) Zbl0064.33002MR0069338
  3. J. K. Hale, Ordinary differential equations, Wiley-Interscience. New York 1969. (1969) Zbl0186.40901MR0419901
  4. P. Hartman, Ordinary differential equations, Wiley & Sons, New York 1964. (1964) Zbl0125.32102MR0171038
  5. A. Kelley, Stability of the center-stable manifold, Ј. Math. Аnal. Аppl. 18 (1967), 336-344. (1967) Zbl0166.08304MR0210998
  6. H. W. Knobloch, F. Kappel, Gewöhnliche Differentialgleichungen, Teubner, Stuttgart 1974. (1974) Zbl0283.34001MR0591708
  7. K. Palmer, Qualitative behavior of a system of ODE near an equilibrium point - А generalization of the Hartman-Grobman theorem, Preprint 372, Inst. f. Аngew. Mathem. Univ. Вonn 1980. (1980) 
  8. V. A. Pliss, Principleof reduction in the theory of the stability of motion, Izv. Аkad. Nauk SSSR, Mat. Ser. 28 (1964), 1297-1324 (in Russian). (1964) MR0190449
  9. S. M. Graff, On the conservation of hyperbolic invariant tori for Hamiltonian systems, Јourn. Diff. Equations 15 (1974), 1-69. (1974) Zbl0257.34048MR0365626

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