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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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The Homotopy Index and Partial Differential Equations

The Homotopy Index and Partial Differential Equations

Rybakowski, Krzysztof P.

Paperback

Series: Universitext

General GardeningGeneral MathematicsGeometry

ISBN10: 3540180672
ISBN13: 9783540180678
Publisher: Springer Nature
Published: Aug 24 1987
Pages: 208
Weight: 0.80
Height: 0.47 Width: 6.69 Depth: 9.61
Language: English
The homotopy index theory was developed by Charles Conley for two- sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi- cal measure of an isolated invariant set, is defined to be the ho- motopy type of the quotient space N /N, where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the exit ramp of N . 1 It is shown that the index is independent of the choice of the in- dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde- generate critical point p with respect to a gradient flow on a com- pact manifold. In fact if the Morse index of p is k, then the homo- topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.

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