Invariant Manifolds in Discrete and Continuous Dynamical Systems

  • Kaspar Nipp

    ETH Zürich, Switzerland
  • Daniel Stoffer

    ETH Zürich, Switzerland
Invariant Manifolds in Discrete and Continuous Dynamical Systems cover

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FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–vi
ContentsDownload pp. vii–ix
Part I Discrete Dynamical Systems – Mapspp. 1–3
1Existencepp. 5–32
2Perturbation and approximationpp. 33–36
3Smoothnesspp. 37–45
4Foliationpp. 46–58
5Smoothness of the foliation with respect to the base pointpp. 59–68
Part II Continuous Dynamical Systems – ODEspp. 69–70
6A general result for the time-T mappp. 71–73
7Invariant manifold resultspp. 74–92
Part III Applicationspp. 93–94
8Fixed points and equilibriapp. 95–100
9The one-step method associated to a linear multistep methodpp. 101–109
10Invariant manifolds for singularly perturbed ODEspp. 110–120
11Runge–Kutta methods applied to singularly perturbed ODEspp. 121–136
12Invariant curves of perturbed harmonic oscillatorspp. 137–155
13Blow-up in singular perturbationspp. 156–186
14Application of Runge–Kutta methods to differential-algbraic equationspp. 187–196
Part IV Appendicesp. 197
AHypotheses and conditions for mapspp. 199–203
BHypotheses and conditions for ODEspp. 204–206
Bibliographypp. 207–214
Indexpp. 215–216