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1
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Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings

100%
Kulczycki M.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 1
1-6
EN
We prove that for every nonempty compact manifold of nonzero dimension no self-homeomorphism and no continuous self-mapping has the uniform pseudo-orbit tracing property. Several relevant counterexamples for recently studied hypotheses are indicated.
2
Content available remote

Properties of dynamical systems with the asymptotic average shadowing property

64%
Kulczycki M., Oprocha P.
Fundamenta Mathematicae
|
2011
|
tom 212
|
nr 1
35-52
EN
This article investigates under what conditions nontransitivity can coexist with the asymptotic average shadowing property. We show that there is a large class of maps satisfying both conditions simultaneously and that it is possible to find such examples even among maps on a compact interval. We also study the limit shadowing property and its relation to the asymptotic average shadowing property.
3
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A class of continua that are not attractors of any IFS

64%
Kulczycki M., Nowak M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2073-2076
EN
This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.
4
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On the connectedness of boundary and complement for domains

51%
Czarnecki A., Kulczycki M., Lubawski W.
Annales Polonici Mathematici
|
2012
|
tom 103
|
nr 2
EN
This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.
5
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On almost specification and average shadowing properties

51%
Kulczycki M., Kwietniak D., Oprocha P.
Fundamenta Mathematicae
|
2014
|
tom 224
|
nr 3
241-278
EN
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.
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