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(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space ℓ 1 ( ℕ ) , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c 0 ( ℕ ) or ℓ p ( ℕ ) , 1 < p < ∞ . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

⊗-product of Markov matrices.

J. P. Lampreia, A. Rica da Silva, J. Sousa Ramos (1988)

Stochastica

In this paper we introduce a ⊗-operation over Markov transition matrices, in the context of subshift of finite type, reproducing symbolic properties of the iterates of the critical point on a one-parameter family of unimodal maps. To the *-product between kneading sequences we associate a ⊗-product between the corresponding Markov matrices.

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