Displaying similar documents to “On the Conley index in Hilbert spaces - a multivalued case”

Fixed point index theory for a class of nonacyclic multivalued maps

Zdzisław Dzedzej

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CONTENTS0. Introduction.....................................................................5I. Homology.........................................................................6II. Multivalued maps...........................................................11III. Chain approximations and index...................................15IV. Chain approximations of decompositions of maps........18V. Index of decompositions for compact polyhedra............26VI. Index of decompositions for compact...

Conley type index and Hamiltonian inclusions

Zdzisław Dzedzej (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.

Connection matrix pairs

David Richeson (1999)

Banach Center Publications

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We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and...