The Homotopy Index and Partial Differential Equations
Springer Berlin (Verlag)
978-3-540-18067-8 (ISBN)
The book presents an extension, due to the present author, of Conley's homotopy index theory to certain (one-sided) semiflows on general (not necessarily locally compact) metric spaces. This permits direct applications to say, parabolic partial differential equations, or functional differential equations. The presentation is self-contained. The subject of the book was previously presented by the author in a series of published papers.
I The homotopy index theory.- 1.1 Local semiflows.- 1.2 The no blow-up condition. Convergence of semiflows.- 1.3 Isolated invariant sets and isolating blocks.- 1.4 Admissibility.- 1.5 Existence of isolating blocks.- 1.6 Homotopies and inclusion induced maps.- 1.7 Index and quasi-index pairs.- 1.8 Some special maps used in the construction of the Morse index.- 1.9 The Categorial Morse index.- 1.10 The homotopy index and its basic properties.- 1.11 Linear semiflows. Irreducibility.- 1.12 Continuation of the homotopy index.- II Applications to partial differential equations.- 2.1 Sectorial operators generated by partial differential operators.- 2.2 Center manifolds and their approximation.- 2.3 The index product formula.- 2.4 A one-dimensional example.- 2.5 Asymptotically linear systems.- 2.6 Estimates at zero and nontrivial solution of elliptic equations.- 2.7 Positive heteroclinic orbits of second-order parabolic equations.- 2.8 A homotopy index continuation method and periodic solutions of second-order gradient systems.- III Selected topics.- 3.1 Repeller-attractor pairs and Morse decompositions.- 3.2 Block pairs and index triples.- 3.3 A Morse equation.- 3.4 The homotopy index and Morse theory on Hilbert manifolds.- 3.5 Continuation of the categorial Morse index along paths.- Bibliographical notes and comments.
| Erscheint lt. Verlag | 24.8.1987 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | XII, 208 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 170 x 244 mm |
| Gewicht | 430 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | convergence • differential equation • Differential operator • Homotopie-Index-Theorie • manifold • Metric Space • partial differential equation • Partielle Differenzialgleichungen |
| ISBN-10 | 3-540-18067-2 / 3540180672 |
| ISBN-13 | 978-3-540-18067-8 / 9783540180678 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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