Displaying similar documents to “Generic points in the cartesian powers of the Morse dynamical system”

Aproximation of Z-cocycles and shift dynamical systems.

I. Filipowicz, J. Kwiatkowski, M. Lemanczyk (1988)

Publicacions Matemàtiques

Similarity:

Let Gbar = G{nt, nt | nt+1, t ≥ 0} be a subgroup of all roots of unity generated by exp(2πi/nt}, t ≥ 0, and let τ: (X, β, μ) O be an ergodic transformation with pure point spectrum Gbar. Given a cocycle φ, φ: X → Z2, admitting an approximation with speed 0(1/n1+ε, ε>0) there exists a Morse cocycle φ such that the corresponding transformations τφ...

Relatively independent joinings and subsystems of W*-dynamical systems

Rocco Duvenhage (2012)

Studia Mathematica

Similarity:

Relatively independent joinings of W*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed point subsystems and compact subsystems. This allows us to obtain characterizations of weak mixing and relative ergodicity, as well as of certain compact subsystems, in terms of joinings.

Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski, Wojciech Mitkowski (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...

Construction of non-constant and ergodic cocycles

Mahesh Nerurkar (2000)

Colloquium Mathematicae

Similarity:

We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...

Tower multiplexing and slow weak mixing

Terrence Adams (2015)

Colloquium Mathematicae

Similarity:

A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity sequences of weak mixing transformations. Namely, given any rigidity sequence for an ergodic measure preserving transformation, there exists a weak mixing transformation which is rigid along the same sequence. This establishes a wide range of rigidity sequences for weakly mixing dynamical...

Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

Y. Derriennic, K. Frączek, M. Lemańczyk, F. Parreau (2008)

Colloquium Mathematicae

Similarity:

Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems...

Ergodic theorem, reversibility and the filling scheme

Yves Derriennic (2010)

Colloquium Mathematicae

Similarity:

The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple...

S-unimodal Misiurewicz maps with flat critical points

Roland Zweimüller (2004)

Fundamenta Mathematicae

Similarity:

We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable...