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1
Content available remote

Construction and properties of the Conley index

100%
Mrozek M.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
29-40
2
Content available remote

From the theorem of Ważewski to computer assisted proofs in dynamics

100%
Mrozek M.
Banach Center Publications
|
1995
|
tom 34
|
nr 1
105-120
3
Content available remote

Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces

100%
Mrozek M.
Fundamenta Mathematicae
|
1994
|
tom 145
|
nr 1
15-37
EN
We present a scheme for constructing various Conley indices for locally defined maps. In particular, we extend the shape index of Robbin and Salamon to the case of a locally defined map in a locally compact Hausdorff space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity property of the fixed point index.
4
Content available remote

Homology of representable sets

64%
Mrozek M., Batko B.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 3
243-252
EN
We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.
5
Content available remote

Set arithmetic and the enclosing problem in dynamics

64%
Mrozek M., Zgliczyński P.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
237-259
EN
We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
6
Content available remote

On a generalization of the Conley index

51%
Mrozek M., Reineck J. F., Srzednicki R.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
157-171
EN
In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain some of the information which is lost on collapse. As an example, is it possible that two repelling periodic orbits which are not homotopic in the punctured plane are related by continuation? Clearly one cannot be continued to the other as periodic orbits, but the index of such a periodic orbit is the same as the index of the disjoint union of two rest points, so the question of continuation as isolated invariant sets is far less obvious.
7
Content available remote

Index pairs and the fixed point index for semidynamical systems with discrete time

50%
Mrozek M.
Fundamenta Mathematicae
|
1989
|
tom 133
|
nr 3
179-194
8
Content available remote

Foreword, Contents

32%
Mischaikow K., Mrozek M., Zgliczyński P.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
1-7
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