The homotopy index and partial differential equations

Krzysztof P. Rybakowski

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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  • 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.

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書名 The homotopy index and partial differential equations
著作者等 Rybakowski, Krzysztof P.
Rybakowski Krzysztof P
シリーズ名 Universitext
出版元 Springer-Verlag
刊行年月 c1987
版表示 Softcover reprint of the original 1st ed. 1987
ページ数 xii, 208 p.
大きさ 25 cm
ISBN 3540180672
NCID BA00952315
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言語 英語
出版国 ドイツ

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