### Note on weakly mixing transformations.

Huse Fatkic (1992)

Aequationes mathematicae

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Huse Fatkic (1992)

Aequationes mathematicae

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R.E. Rice (1978)

Aequationes mathematicae

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J.A. Lester (1982)

Aequationes mathematicae

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Daniel M. Kane (2007)

Colloquium Mathematicae

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We construct a class of transformations similar to the Pascal transformation, except for the use of spacers, and show that these transformations are weakly mixing.

Amos Koeller, Rodney Nillsen, Graham Williams (2007)

Colloquium Mathematicae

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Let 𝕋 denote the set of complex numbers of modulus 1. Let v ∈ 𝕋, v not a root of unity, and let T: 𝕋 → 𝕋 be the transformation on 𝕋 given by T(z) = vz. It is known that the problem of calculating the outer measure of a T-invariant set leads to a condition which formally has a close resemblance to Carathéodory's definition of a measurable set. In ergodic theory terms, T is not weakly mixing. Now there is an example, due to Kakutani, of a transformation ψ̃ which is weakly mixing but...

J.A. Lester (1985)

Aequationes mathematicae

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Piotr Oprocha, Guohua Zhang (2011)

Studia Mathematica

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We introduce the concept of weakly mixing sets of order n and show that, in contrast to weak mixing of maps, a weakly mixing set of order n does not have to be weakly mixing of order n + 1. Strictly speaking, we construct a minimal invertible dynamical system which contains a non-trivial weakly mixing set of order 2, whereas it does not contain any non-trivial weakly mixing set of order 3. In dimension one this difference is not that much visible, since we prove that...

Jack Clark, Karl David (1981)

Aequationes mathematicae

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P.T. Campos, K. Tenenblat (1994)

Geometric and functional analysis

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V.N. Dubinin (1993)

Geometric and functional analysis

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J. D. Emery, P. Szeptycki (1973)

Annales Polonici Mathematici

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Claudi Alsina (1991)

Aequationes mathematicae

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Alexandre I. Danilenko (2008)

Studia Mathematica

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Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation T which is conjugate to T². Moreover, it is proved that for each odd q, there is such a T commuting with a transformation of order q. For any n, we show the existence of a weakly mixing T conjugate to T² and whose rank is finite and greater than n.