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On disjointness properties of some smooth flows

Krzysztof Frączek, Mariusz Lemańczyk (2005)

Fundamenta Mathematicae

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...

On functions with bounded remainder

P. Hellekalek, Gerhard Larcher (1989)

Annales de l'institut Fourier

Let T : / / be a von Neumann-Kakutani q - adic adding machine transformation and let ϕ C 1 ( [ 0 , 1 ] ) . Put ϕ n ( x ) : = ϕ ( x ) + ϕ ( T x ) + ... + ϕ ( T n - 1 x ) , x / , n . We study three questions:1. When will ( ϕ n ( x ) ) n 1 be bounded?2. What can be said about limit points of ( ϕ n ( x ) ) n 1 ? 3. When will the skew product ( x , y ) ( T x , y + ϕ ( x ) ) be ergodic on / × ?

On group extensions of 2-fold simple ergodic actions

Artur Siemaszko (1994)

Studia Mathematica

Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.

On invariant elements for positive operators.

R. Zaharopol (1997)

Revista Matemática de la Universidad Complutense de Madrid

In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...

On invariant measures for the tend map.

Francesc Bofill (1988)

Stochastica

The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.

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