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