A large set containing few orbits of measure preserving transformations. (Summary).
A large set containing few orbits of measure preserving transformations.
The problem of -simple spectrum for ergodic group automorphisms
Toeplitz flows with pure point spectrum
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.
Extreme operators on AL-spaces
Cyclic approximation of analytic cocycles over irrational rotations
Spectral properties of skew-product diffeomorphisms of tori
Generic smooth cocycles of degree zero over irrational rotations
If a rotation α of has unbounded partial quotients then “most” of its skew-product diffeomorphic extensions to the 2-torus × defined by 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 cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic cocycles the speed can be improved to o(1/(nlogn)). For generic...
Quasi-uniform convergence in compact dynamical systems
Some constructions of strictly ergodic non-regular Toeplitz flows
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.
Most monothetic extensions are rank-1
Extreme contractions on C(X) and
On strong mixing and weak convergence for groups of operators
Two-sided nonsingular transformations
On norm attaining operators acting from to C (S)
On norm attaining operators acting on - spaces
Quelques remarques sur les facteurs des systèmes dynamiques gaussiens
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 is generating.
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