Displaying similar documents to “Some remarks on tubular neighborhoods and gluing in Morse-Floer homology”

The configuration space of gauge theory on open manifolds of bounded geometry

Jürgen Eichhorn, Gerd Heber (1997)

Banach Center Publications

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We define suitable Sobolev topologies on the space 𝒞 P ( B k , f ) of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.

Conley index for set-valued maps: from theory to computation

Tomasz Kaczynski (1999)

Banach Center Publications

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Recent results on the Conley index theory for discrete multi-valued dynamical systems with their consequences for the computation of the index for representable maps are recapitulated. The terminology is simplified with respect to previous presentations, some superfluous hypotheses are abandoned and some conclusions are proved in a simpler way.

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...

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae

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We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology. ...

Smoothness of unordered curves in two-dimensional strongly competitive systems

Janusz Mierczyński (1999)

Applicationes Mathematicae

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It is known that in two-dimensional systems of ODEs of the form i = x i f i ( x ) with ∂ f i / ∂ x j < 0 (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class C 1 .

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.