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Isometric extensions, 2-cocycles and ergodicity of skew products

100%

Danilenko A. I., Lemańczyk M.

Studia Mathematica

1999

tom 137

nr 2

123-142

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 $T_α$.

Invariant densities for C¹ maps

100%

N. Quas A.

Studia Mathematica

1996

tom 120

nr 1

83-88

We consider the set of $C^1$ expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of $C^1$ expanding maps with the $C^1$ topology. This is in contrast with results for $C^2$ or $C^{1+ε}$ maps, where the invariant densities can be shown to be continuous.

Compact Global Chaotic Attractors of Discrete Control Systems

75%

Cheban D.

Nonautonomous Dynamical Systems

2014

tom 1

The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles).

Ograniczanie wyników

2 Studia Mathematica

1 Nonautonomous Dynamical Systems

1 Cheban D.

1 Danilenko A. I.

1 Lemańczyk M.

1 N. Quas A.

1 2013

1 1999

1 1996

Wyniki wyszukiwania

Isometric extensions, 2-cocycles and ergodicity of skew products

Invariant densities for C¹ maps

Compact Global Chaotic Attractors of Discrete Control Systems