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1
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Cohomology groups, multipliers and factors in ergodic theory

100%
Lemańczyk M.
Studia Mathematica
|
1997
|
tom 122
|
nr 3
275-288
EN
The problem of compact factors in ergodic theory and its relationship with the problem of extending a cocycle to a cocycle of a larger action are studied.
2
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Sur l'absence de mélange pour des flots spéciaux au-dessus d'une rotation irrationnelle

100%
Lemańczyk M.
Colloquium Mathematicum
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2000
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tom 84/85
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nr 1
29-41
EN
We prove the absence of mixing for special flows built over (1) an irrational rotation and under a function whose Fourier coefficients are of order O(1/|n|), and (2) an irrational rotation (satisfying a diophantine condition) and under a function having a finite number of singularities of a logarithmic type. These results generalize two theorems of Kochergin.
3
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Some new cases of realization of spectral multiplicity function for ergodic transformations

64%
Katok A., Lemańczyk M.
Fundamenta Mathematicae
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2009
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tom 206
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nr 1
185-215
EN
Given a countable Abelian group 𝔾, its automorphism w for which $w^{M} = Id$, and a subgroup 𝔽 ⊂ 𝔾 we define $M(𝔾,w,𝔽) = {♯({w^{i}χ: i ∈ ℤ ∩ 𝔽): χ ∈ 𝔽∖{0}}$. We prove that each finite set of the form M(𝔾,w,𝔽) ∪ {2} is realized as the set of essential values of the multiplicity function of the Koopman operator of some weakly mixing automorphism.
4
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On symmetric logarithm and some old examples in smooth ergodic theory

64%
Frączek K., Lemańczyk M.
Fundamenta Mathematicae
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2003
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tom 180
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nr 3
241-255
EN
We give a positive answer to the problem of existence of smooth weakly mixing but not mixing flows on some surfaces. More precisely, on each compact connected surface whose Euler characteristic is even and negative we construct smooth weakly mixing flows which are disjoint in the sense of Furstenberg from all mixing flows and from all Gaussian flows.
5
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Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

51%
Derriennic Y., Frączek K., Lemańczyk M., Parreau F.
Colloquium Mathematicum
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2008
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tom 110
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nr 1
81-115
EN
Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems determined by stationary ergodic symmetric α-stable processes are shown to belong to the ELF class.
6
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On the multiplicity function of ergodic group extensions of rotations

51%
R. Goodson G., Kwiatkowski J., Lemańczyk M., Liardet P.
Studia Mathematica
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1992
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tom 102
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nr 2
157-174
EN
For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.
7
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Semisimplicity, joinings and group extensions

51%
Del Junco A., Lemańczyk M., Mentzen M. K.
Studia Mathematica
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1994-1995
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tom 112
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nr 2
141-164
EN
We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].
8
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Constructions of cocycles over irrational rotations

51%
Bułatek W., Lemańczyk M., Rudolph D.
Studia Mathematica
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1997
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tom 125
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nr 1
1-11
EN
We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.
9
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On the rank of a class of bijective substitutions

32%
Goodson G. R., Lemańczyk M.
Studia Mathematica
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1990
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tom 96
|
nr 3
219-230
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