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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Some properties of coalescent automorphisms of a Lebesgue space

100%
Kamiński B.
Commentationes Mathematicae
|
1980
|
tom 21
|
nr 1
EN
The article contains no abstract
2

On abelian groups of transformations with completely positive entropy

88%
Kamiński B.
Commentationes Mathematicae
|
1980
|
tom 21
|
nr 1
EN
The article contains no abstract
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Relative generators for the action of a countable abelian group on a Lebesgue space

88%
Kamiński B.
Banach Center Publications
|
1989
|
tom 23
|
nr 1
75-81
4
Content available remote

On the directional entropy for ℤ²-actions on a Lebesgue space

64%
Kamiński B., Park K. K.
Studia Mathematica
|
1999
|
tom 133
|
nr 1
39-51
EN
We define the concept of directional entropy for arbitrary $ℤ^2$-actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.
5
Content available remote

On extremal and perfect σ-algebras for flows

64%
Kamiński B., Kowalski Z. S.
Studia Mathematica
|
1998
|
tom 129
|
nr 2
179-183
EN
It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.
6
Content available remote

Relatively perfect σ-algebras for flows

64%
Blanchard F., Kamiński B.
Studia Mathematica
|
1995
|
tom 114
|
nr 1
71-85
EN
We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
7
Content available remote

Spectrum of multidimensional dynamical systems with positive entropy

64%
Kamiński B., Liardet P.
Studia Mathematica
|
1994
|
tom 108
|
nr 1
77-85
EN
Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^d$-action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^∞$-actions. Next, using its relative version, we extend to $ℤ^∞$-actions some other general results connecting spectrum and entropy.
8
Content available remote

On the directional entropy of ℤ²-actions generated by cellular automata

64%
Courbage M., Kamiński B.
Studia Mathematica
|
2002
|
tom 153
|
nr 3
285-295
EN
We show that for any cellular automaton (CA) ℤ²-action Φ on the space of all doubly infinite sequences with values in a finite set A, determined by an automaton rule $F = F_{[l,r]}$, l,r ∈ ℤ, l ≤ r, and any Φ-invariant Borel probability measure, the directional entropy $h_{v⃗}(Φ)$, v⃗= (x,y) ∈ ℝ², is bounded above by $max(|z_{l}|,|z_{r}|) log #A$ if $z_{l}z_{r} ≥ 0$ and by $|z_{r} - z_{l}|$ in the opposite case, where $z_{l} = x + ly$, $z_{r} = x + ry$. We also show that in the class of permutative CA-actions the bounds are attained if the measure considered is uniform Bernoulli.
9
Content available remote

On extremal and perfect σ-algebras for $ℤ^{d}$-actions on a Lebesgue space

52%
Kamiński B., Kowalski Z. S., Liardet P.
Studia Mathematica
|
1997
|
tom 124
|
nr 2
173-178
EN
We show that for every positive integer d there exists a $ℤ^d$-action and an extremal σ-algebra of it which is not perfect.
10
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

A representation theorem for perfect partitions of $Z^2$-actions with finite entropy

50%
Kamiński B.
Colloquium Mathematicum
|
1988
|
tom 56
|
nr 1
121-127
11
Content available remote

An axiomatic definition of the entropy of a $Z^{d}$-action on a Lebesgue space

44%
Kamiński B.
Studia Mathematica
|
1990
|
tom 96
|
nr 2
135-144
12
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Regular generators for multidimensional dynamical systems

32%
Kamiński B., Kobus M.
Colloquium Mathematicum
|
1985-1986
|
tom 50
|
nr 2
263-270
13
Content available remote

On regular generator of Z²-actions in exhaustive partitions

32%
Kamiński B.
Studia Mathematica
|
1987
|
tom 85
|
nr 1
17-26
14
Content available remote

Generators of perfect σ-algebras of $Z^{d}$-actions

32%
Kamiński B.
Studia Mathematica
|
1991
|
tom 99
|
nr 1
11-21
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