منابع مشابه
On Lyapunov Exponents of Continuous Schrödinger Cocycles over Irrational Rotations
In this note, we consider continuous, SL(2,R)-valued, Schrödinger cocycles over irrational rotations. We prove two generic results on the Lyapunov exponents which improve the corresponding ones contained in [3].
متن کاملCompletely Squashable Smooth Ergodic Cocycles over Irrational Rotations
Let α be an irrational number and the trasformation Tx 7→ x+ α mod 1, x ∈ [0, 1), represent an irrational rotation of the unit circle. We construct an ergodic and completely squashable smooth real extension, i.e. we find a real analytic or k time continuously differentiable real function F such that for every λ 6= 0 there exists a commutor Sλ of T such that F ◦Sλ is T -cohomologous to λφ and th...
متن کاملOn Spectral Properties of Skew Products over Irrational Rotations
In the process of obtaining these results we make some observations, which may be of more general interest, concerning the problems of singularity and continuity of the spectral types of skew products. See §2 and §4. Our approach is based on the method of approximations as formulated by Katok and Stepin [4, 5] and later developed and modified by a number of authors [1, 3, 8, 9]. For the continu...
متن کاملIrrational rotations motivate measurable sets
In 1914 Constantin Carathéodory gave his definition of a measurable set, a definition that is crucial in the general theory of integration. This is because a “primitive” notion of area or measure, on a smaller family of sets, can be extended to the larger family of measurable sets, and it is this larger family that has the necessary properties for a natural and complete theory of integration. T...
متن کاملA renormalization approach to irrational rotations
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle β 7→ {α+ β}, α ∈ R \ Q. In particular we obtain sharp results for the diffusion of the walk on Z generated by the location of points of the sequence {nα + β} on a binary partition of the unit interval. Finally we give some application...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1997
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-126-3-253-271