Krzysztof Rybakowski

The Homotopy Index and Partial Differential Equations

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Universitext
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-18067-8
• 1987.
• Seitenzahl: 224
• Erscheinungstermin: 24. August 1987
• Englisch
• Abmessung: 244mm x 170mm x 13mm
• Gewicht: 395g
• ISBN-13: 9783540180678
• ISBN-10: 3540180672
• Artikelnr.: 27172370

Inhaltsangabe

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.