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Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback

About this Title

Tibor Krisztin, University of Szeged, Bolyai Institute, Hungary, Hans-Otto Walther, Universität Giessen, Giessen, Germany and Jianhong Wu, York University, North York, ON, Canada

Publication: Fields Institute Monographs
Publication Year: 1999; Volume 11
ISBNs: 978-0-8218-1074-3 (print); 978-1-4704-3138-9 (online)
DOI: https://doi.org/10.1090/fim/011
MathSciNet review: MR1719128
MSC: Primary 34K99; Secondary 34K20, 34K25, 37C70

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Table of Contents

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Front/Back Matter

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Chapters

• Chapter 1. Introduction
• Chapter 2. The delay differential equation and the hypotheses
• Chapter 3. The separatrix
• Chapter 4. The leading unstable set of the origin
• Chapter 5. Oscillation frequencies
• Chapter 6. Graph representations
• Chapter 7. Dynamics on $\overline W$ and disk representation of $\overline W \cap S$
• Chapter 8. Minimal linear instability of the periodic orbit $\mathcal O$
• Chapter 9. Smoothness of $W \cap S$ in case $\mathcal O$ is hyperbolic
• Chapter 10. Smoothness of $W \cap S$ in case $\mathcal O$ is not hyperbolic
• Chapter 11. The unstable set of $\mathcal O$ contains the nonstationary points of bd$W$
• Chapter 12. bd$W$ contains the unstable set of the periodic orbit $\mathcal O$
• Chapter 13. $H \cap \overline W$ is smooth near $p_0$
• Chapter 14. Smoothness of $\overline W$, bd$W$ and $\overline W \cap S$
• Chapter 15. Homeomorphisms from bd$W$ onto the sphere and the cylinder
• Chapter 16. Homeomorphisms from $\overline W$ onto the closed ball and the solid cylinder
• Chapter 17. Resumé
• Appendix I. Equivalent norms, invariant manifolds, Poincaré maps and asymptotic phases
• Appendix II. Smooth center-stable manifolds for $C^1$-maps
• Appendix III. Smooth generalized center-unstable manifolds for $C^1$-maps
• Appendix IV. Invariant cones close to neutrally stable fixed points with 1-dimensional center spaces
• Appendix V. Unstable sets of periodic orbits
• Appendix VI. A discrete Lyapunov functional and a-priori estimates
• Appendix VII. Floquet multipliers for a class of linear periodic delay differential equations
• Appendix VIII. Some results from topology