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Ratner's property for special flows over irrational rotations under functions of bounded variation. II

100%

Kanigowski A.

Colloquium Mathematicum

2014

tom 136

nr 1

125-147

We consider special flows over the rotation on the circle by an irrational α under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the devil's staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that α has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy the weak Ratner property. Moreover, we provide a sufficient condition on the roof function for stability of Ratner's cocycle property of the resulting special flow.

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

63%

Kanigowski A., Kryszewski W.

Open Mathematics

2012

tom 10

nr 6

2240-2263

We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Kanigowski A.

1 Kryszewski W.

1 2014

1 2012

Wyniki wyszukiwania

Ratner's property for special flows over irrational rotations under functions of bounded variation. II

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators