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Fixed point index theory for a class of nonacyclic multivalued maps

100%
Dzedzej Z.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 0. Introduction.....................................................................5 I. Homology.........................................................................6 II. Multivalued maps...........................................................11 III. Chain approximations and index...................................15 IV. Chain approximations of decompositions of maps........18 V. Index of decompositions for compact polyhedra............26 VI. Index of decompositions for compact ANR's.................31 VII. Index of decompositions for arbitrary ANR's................38 VIII. Applications of the index to multivalued maps............42 IX. The Nielsen theory.......................................................47 References.......................................................................52
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On the Conley index in Hilbert spaces - a multivalued case

96%
Dzedzej Z.
Banach Center Publications
|
2007
|
tom 77
|
nr 1
61-68
EN
We introduce the cohomological Conley type index theory for multivalued flows generated by vector fields which are compact and convex-valued perturbations of some linear operators.
3
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On the Nielsen fixed point theory for multivalued mappings

96%
Dzedzej Z.
Banach Center Publications
|
1999
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tom 49
|
nr 1
69-75
EN
We present J. Jezierski's approach to the Nielsen fixed point theory for a broad class of multivalued mappings [Je1]. We also describe some generalizations and different techniques existing in the literature.
4
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Equivariant degree of convex-valued maps applied to set-valued BVP

96%
Dzedzej Z.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2173-2186
EN
An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.
5
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Module structure in Conley theory with some applications

96%
Dzedzej Z.
Banach Center Publications
|
2014
|
tom 101
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nr 1
59-76
EN
A multiplicative structure in the cohomological version of Conley index is described following a joint paper by the author with K. Gęba and W. Uss. In the case of equivariant flows we apply a normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is applied then to obtain a mountain pass type theorem. Another illustrative application is a result on multiple bifurcations for some elliptic PDE.
6
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Connection matrix theory for discrete dynamical systems

61%
Bartłomiejczyk P., Dzedzej Z.
Banach Center Publications
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1999
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tom 47
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nr 1
67-78
EN
In [C] and [F1] the connection matrix theory for Morse decomposition is developed in the case of continuous dynamical systems. Our purpose is to study the case of discrete time dynamical systems. The connection matrices are matrices between the homology indices of the sets in the Morse decomposition. They provide information about the structure of the Morse decomposition; in particular, they give an algebraic condition for the existence of connecting orbit set between different Morse sets.
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