Displaying similar documents to “Useful properties of index pairs for upper semicontinuous multivalued dynamical systems.”

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.

The Nielsen coincidence theory on topological manifolds

Jerzy Jezierski (1993)

Fundamenta Mathematicae

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We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.

Nielsen theory of transversal fixed point sets (with an appendix: C ∞ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

On the Schauder fixed point theorem

Lech Górniewicz, Danuta Rozpłoch-Nowakowska (1996)

Banach Center Publications

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The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.