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Displaying similar documents to “Some remarks on the discrete Morse-Smale characteristic.”

Critical points of asymptotically quadratic functions

Michal Fečkan (1995)

Annales Polonici Mathematici

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Existence results for critical points of asymptotically quadratic functions defined on Hilbert spaces are studied by using Morse-Conley index and pseudomonotone mappings. Applications to differential equations are given.

On foundations of the Conley index theory

Roman Srzednicki (1999)

Banach Center Publications

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The Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the...

Existence results for the prescribed Scalar curvature on S 3

Randa Ben Mahmoud, Hichem Chtioui (2011)

Annales de l’institut Fourier

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This paper is devoted to the existence of conformal metrics on S 3 with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.

Reconstructing the global dynamics of attractors via the Conley index

Christopher McCord (1999)

Banach Center Publications

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Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy...