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1
Content available remote

Isometric extensions, 2-cocycles and ergodicity of skew products

100%
Danilenko A. I., Lemańczyk M.
Studia Mathematica
|
1999
|
tom 137
|
nr 2
123-142
EN
We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_α$ and admits a prescribed subgroup in the centralizer of $T_α$.
2
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On disjointness properties of some smooth flows

100%
Frączek K., Lemańczyk M.
Fundamenta Mathematicae
|
2005
|
tom 185
|
nr 2
117-142
EN
Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange transformations and under functions of bounded variation are disjoint from mixing flows; ∙ ergodic components of flows coming from billiards on rational polygons are disjoint from mixing flows; ∙ smooth ergodic flows of compact orientable smooth surfaces having only non-degenerate saddles as isolated critical points (and having a "good" transversal) are disjoint from mixing and from Gaussian flows.
3
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The centralizer of ergodic theory group extensions

100%
Kwiatkowski J., Lemańczyk M.
Banach Center Publications
|
1989
|
tom 23
|
nr 1
455-463
4
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On the multiplicity function of ergodic group extensions, II

100%
Kwiatkowski J., Lemańczyk M.
Studia Mathematica
|
1995
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tom 116
|
nr 3
207-215
EN
For an arbitrary set $A ⊆ ℕ^+$ containing 1, an ergodic automorphism T whose set of essential values of the multiplicity function is equal to A is constructed. If A is additionally finite, T can be chosen to be an analytic diffeomorphism on a finite-dimensional torus.
5
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Simple systems are disjoint from Gaussian systems

100%
del Junco A., Lemańczyk M.
Studia Mathematica
|
1999
|
tom 133
|
nr 3
249-256
EN
We prove the theorem promised in the title. Gaussians can be distinguished from simple maps by their property of divisibility. Roughly speaking, a system is divisible if it has a rich supply of direct product splittings. Gaussians are divisible and weakly mixing simple maps have no splittings at all so they cannot be isomorphic. The proof that they are disjoint consists of an elaboration of this idea, which involves, among other things, the notion of virtual divisibility, which is, more or less, divisibility up to distal extensions. The theory of Kronecker Gaussians also plays a crucial role.
6
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On analytic flows on the torus which are disjoint from systems of probabilistic origin

100%
Lemańczyk M., Wysokińska M.
Fundamenta Mathematicae
|
2007
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tom 195
|
nr 2
97-124
EN
We describe two methods of obtaining analytic flows on the torus which are disjoint from dynamical systems induced by some classical stationary processes.
7
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A cut salad of cocycles

81%
Aaronson J., Lemańczyk M., Volný D.
Fundamenta Mathematicae
|
1998
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tom 157
|
nr 2-3
99-119
EN
We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed.
8
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Gaussian automorphisms whose ergodic self-joinings are Gaussian

81%
Lemańczyk M., Parreau F., Thouvenot J. P.
Fundamenta Mathematicae
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2000
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tom 164
|
nr 3
253-293
EN
 We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class.  We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors. This and an elaborate study of isomorphisms between classical factors of Gaussian automorphisms allow us to give a complete solution of the disjointness problem between a Gaussian automorphism whose ergodic self-joinings remain Gaussian and an arbitrary Gaussian automorphism.
9
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Semisimple extensions of irrational rotations

81%
Lemańczyk M., Mentzen M., Nakada H.
Studia Mathematica
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2003
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tom 156
|
nr 1
31-57
EN
We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.
10
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Quelques remarques sur les facteurs des systèmes dynamiques gaussiens

81%
Iwanik A., Lemańczyk M., de la Rue T., de Sam Lazaro J.
Studia Mathematica
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1997
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tom 125
|
nr 3
247-254
EN
We study the factors of Gaussian dynamical systems which are generated by functions depending only on a finite number of coordinates. As an application, we show that for Gaussian automorphisms with simple spectrum, the partition ${(X_0 ≤ 0), (X_0 > 0)}$ is generating.
11
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The sequence entropy for Morse shifts and some counterexamples

60%
Lemańczyk M.
Studia Mathematica
|
1985
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tom 82
|
nr 3
221-241
12
Content available remote

Entropy of Gaussian actions for countable Abelian groups

60%
Lemańczyk M.
Fundamenta Mathematicae
|
1998
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tom 157
|
nr 2-3
277-286
13
Content available remote

Rank is not a spectral invariant

50%
Ferenczi S., Lemańczyk M.
Studia Mathematica
|
1991
|
tom 98
|
nr 3
227-230
14
Content available remote

Factors of coalescent automorphisms

40%
Lemańczyk M.
Studia Mathematica
|
1988
|
tom 89
|
nr 2
159-168
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