Wyniki wyszukiwania

1

Toeplitz flows with pure point spectrum

100%

Iwanik A.

Studia Mathematica

|

1996

|

tom 118

|

nr 1

27-35

EN

We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.

2

Spectral properties of skew-product diffeomorphisms of tori

100%

Iwanik A.

Colloquium Mathematicum

|

1997

|

tom 72

|

nr 2

223-235

3

Cyclic approximation of analytic cocycles over irrational rotations

100%

Iwanik A.

Colloquium Mathematicum

|

1996

|

tom 70

|

nr 1

73-78

4

Generic smooth cocycles of degree zero over irrational rotations

100%

Iwanik A.

Studia Mathematica

|

1995

|

tom 115

|

nr 3

241-250

EN

If a rotation α of 𝕋 has unbounded partial quotients then "most" of its skew-product diffeomorphic extensions to the 2-torus 𝕋 × 𝕋 defined by $C^1$ cocycles of topological degree zero enjoy nontrivial ergodic properties. In fact they admit a cyclic approximation with speed o(1/n) and have nondiscrete (simple) spectrum. Similar results are obtained for $C^r$ cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic $C^1$ cocycles the speed can be improved to o(1/(nlogn)). For generic α and generic $C^r$ cocycles (r = 1,...,∞) the spectral measure of the skew product has a continuous component and Hausdorff dimension zero.

5

Ergodicity for piecewise smooth cocycles over toral rotations

100%

Iwanik A.

Fundamenta Mathematicae

|

1998

|

tom 157

|

nr 2-3

235-244

EN

Let α be an ergodic rotation of the d-torus $\mathbb{T}^d = ℝ^d/ℤ^d$. For any piecewise smooth function $f: \mathbb{T}^d → ℝ$ with sufficiently regular pieces the unitary operator Vh(x) = exp(2π if(x))h(x + α) acting on $L^2(\mathbb{T}^d)$ is shown to have a continuous non-Dirichlet spectrum if the gradient of f has nonzero integral. In particular, the resulting skew product $S_f: \mathbb{T}^{d+1} → \mathbb{T}^{d+1}$ must be ergodic. If in addition α is sufficiently well approximated by rational vectors and f is represented by a linear function with noninteger coefficients then the spectrum of V is singular. In the case d = 1 our technique allows us to extend Pask's result on ergodicity of cylinder flows on T×ℝ to arbitrary piecewise absolutely continuous real-valued cocycles f satisfying ʃf = 0 and ʃf' ≠ 0.

6

Structure of mixing and category of complete mixing for stochastic operators

64%

Iwanik A., Rębowski R.

Annales Polonici Mathematici

|

1991-1992

|

tom 56

|

nr 3

233-242

EN

Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak compactness. Finally, it is shown that most stochastic operators are completely mixing and that the same holds for convolution stochastic operators on l.c.a. groups.

7

Some constructions of strictly ergodic non-regular Toeplitz flows

64%

Iwanik A., Lacroix Y.

Studia Mathematica

|

1994

|

tom 110

|

nr 2

191-203

EN

We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.

8

Most monothetic extensions are rank-1

64%

Iwanik A., Serafin J.

Colloquium Mathematicum

|

1993

|

tom 66

|

nr 1

63-76

9

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Independent sets of transitive points

63%

Iwanik A.

Banach Center Publications

|

1989

|

tom 23

|

nr 1

277-282

10

Quelques remarques sur les facteurs des systèmes dynamiques gaussiens

52%

Iwanik A., Lemańczyk M., de la Rue T., de Sam Lazaro J.

Studia Mathematica

|

1997

|

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

Propriétés topologiques et combinatoires des échelles de numération

52%

Barat G., Downarowicz T., Iwanik A., Liardet P.

Colloquium Mathematicum

|

2000

|

tom 84/85

|

nr 2

285-306

EN

Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.

12

Representation of operators on $L^1$-spaces by nondirect product measures

51%

Iwanik A.

Colloquium Mathematicum

|

1982

|

tom 47

|

nr 1

91-95

13

Multiple recurrence for discrete time Markov processes. II

45%

Downarowicz T., Iwanik A.

Colloquium Mathematicum

|

1988

|

tom 55

|

nr 2

311-316

14

Independence with respect to families of characters

44%

Iwanik A., Mioduszewski J.

Colloquium Mathematicum

|

1988

|

tom 56

|

nr 2

383-392

15

Weak convergence and weighted averages for groups of operators

44%

Iwanik A.

Colloquium Mathematicum

|

1979

|

tom 42

|

nr 1

241-254

16

Multiplicative operators on symmetric commutative algebras

44%

Iwanik A.

Colloquium Mathematicum

|

1977

|

tom 37

|

nr 1

75-79

17

Quasi-uniform convergence in compact dynamical systems

38%

Downarowicz T., Iwanik A.

Studia Mathematica

|

1988

|

tom 89

|

nr 1

11-25

18

Independent subalgebras of a general algebra

38%

Głazek K., Iwanik A.

Colloquium Mathematicum

|

1974

|

tom 29

|

nr 2

189-194

19

Weyl almost periodic points in topological dynamics

38%

Iwanik A.

Colloquium Mathematicum

|

1988

|

tom 56

|

nr 1

107-119

20

Pointwise induced semigroups of σ-endomorphisms

38%

Iwanik A.

Colloquium Mathematicum

|

1977-1978

|

tom 38

|

nr 1

27-35

Ograniczanie wyników

Toeplitz flows with pure point spectrum

Spectral properties of skew-product diffeomorphisms of tori

Cyclic approximation of analytic cocycles over irrational rotations

Generic smooth cocycles of degree zero over irrational rotations

Ergodicity for piecewise smooth cocycles over toral rotations

Structure of mixing and category of complete mixing for stochastic operators

Some constructions of strictly ergodic non-regular Toeplitz flows

Most monothetic extensions are rank-1

Independent sets of transitive points

Quelques remarques sur les facteurs des systèmes dynamiques gaussiens

Propriétés topologiques et combinatoires des échelles de numération

Representation of operators on $L^1$-spaces by nondirect product measures

Multiple recurrence for discrete time Markov processes. II

Independence with respect to families of characters

Weak convergence and weighted averages for groups of operators

Multiplicative operators on symmetric commutative algebras

Quasi-uniform convergence in compact dynamical systems

Independent subalgebras of a general algebra

Weyl almost periodic points in topological dynamics

Pointwise induced semigroups of σ-endomorphisms