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Invariant scrambled sets and maximal distributional chaos

Xinxing Wu, Peiyong Zhu (2013)

Annales Polonici Mathematici

For the full shift (Σ₂,σ) on two symbols, we construct an invariant distributionally ϵ-scrambled set for all 0 < ϵ < diam Σ₂ in which each point is transitive, but not weakly almost periodic.

Inverse limit of M -cocycles and applications

Jan Kwiatkowski (1998)

Fundamenta Mathematicae

For any m, 2 ≤ m < ∞, we construct an ergodic dynamical system having spectral multiplicity m and infinite rank. Given r > 1, 0 < b < 1 such that rb > 1 we construct a dynamical system (X, B, μ, T) with simple spectrum such that r(T) = r, F*(T) = b, and C ( T ) / w c l T n : n ∈ ℤ = ∞

Involutivity degree of a distribution at superdensity points of its tangencies

Silvano Delladio (2021)

Archivum Mathematicum

Let Φ 1 , ... , Φ k + 1 (with k ≥ 1 ) be vector fields of class C k in an open set U ⊂ N + m , let 𝕄 be a N -dimensional C k submanifold of U and define 𝕋 : = { z ∈ 𝕄 : Φ 1 ( z ) , ... , Φ k + 1 ( z ) ∈ T z 𝕄 } where T z 𝕄 is the tangent space to 𝕄 at z . Then we expect the following property, which is obvious in the special case when z 0 is an interior point (relative to 𝕄 ) of 𝕋 : If z 0 ∈ 𝕄 is a ( N + k ) -density point (relative to 𝕄 ) of 𝕋 then all the iterated Lie brackets of order less or equal to k ...

Irreducible Markov systems on Polish spaces

Katarzyna Horbacz, Tomasz Szarek (2006)

Studia Mathematica

Contractive Markov systems on Polish spaces which arise from graph directed constructions of iterated function systems with place dependent probabilities are considered. It is shown that their stability may be studied using the concentrating methods developed by the second author [Dissert. Math. 415 (2003)]. In this way Werner's results obtained in a locally compact case [J. London Math. Soc. 71 (2005)] are extended to a noncompact setting.

Isomorphic random Bernoulli shifts

V. Gundlach, G. Ochs (2000)

Colloquium Mathematicae

We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.

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