Displaying similar documents to “On new spectral multiplicities for ergodic maps”

Conjugacies between ergodic transformations and their inverses

Geoffrey Goodson (2000)

Colloquium Mathematicae

Similarity:

We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation S T = T - 1 S . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of S 2 . In particular, S 2 has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace f ∈ L 2 ( X , ℱ , μ ) : f ( T 2 x ) = f ( x ) . For S and T ergodic satisfying this equation further constraints...

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...

On weakly mixing and doubly ergodic nonsingular actions

Sarah Iams, Brian Katz, Cesar E. Silva, Brian Street, Kirsten Wickelgren (2005)

Colloquium Mathematicae

Similarity:

We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving...

Bergelson's theorem for weakly mixing C*-dynamical systems

Rocco Duvenhage (2009)

Studia Mathematica

Similarity:

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.

Weak mixing of a transformation similar to Pascal

Daniel M. Kane (2007)

Colloquium Mathematicae

Similarity:

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.

Spectral properties of ergodic dynamical systems conjugate to their composition squares

Geoffrey R. Goodson (2007)

Colloquium Mathematicae

Similarity:

Let S and T be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation ST = T²S are given for T ergodic and also when Tⁿ = I for some n>2. These ideas are used to construct examples of ergodic automorphisms S with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.

Weak almost periodicity of L 1 contractions and coboundaries of non-singular transformations

Isaac Kornfeld, Michael Lin (2000)

Studia Mathematica

Similarity:

It is well known that a weakly almost periodic operator T in a Banach space is mean ergodic, and in the complex case, also λT is mean ergodic for every |λ|=1. We prove that a positive contraction on L 1 is weakly almost periodic if (and only if) it is mean ergodic. An example shows that without positivity the result is false. In order to construct a contraction T on a complex L 1 such that λT is mean ergodic whenever |λ|=1, but T is not weakly almost periodic, we prove the following: Let...

Disjointness properties for Cartesian products of weakly mixing systems

Joanna Kułaga-Przymus, François Parreau (2012)

Colloquium Mathematicae

Similarity:

For n ≥ 1 we consider the class JP(n) of dynamical systems each of whose ergodic joinings with a Cartesian product of k weakly mixing automorphisms (k ≥ n) can be represented as the independent extension of a joining of the system with only n coordinate factors. For n ≥ 2 we show that, whenever the maximal spectral type of a weakly mixing automorphism T is singular with respect to the convolution of any n continuous measures, i.e. T has the so-called convolution singularity property...

Ergodic properties of skew products withfibre maps of Lasota-Yorke type

Zbigniew Kowalski (1994)

Applicationes Mathematicae

Similarity:

We consider the skew product transformation T(x,y)= (f(x), T e ( x ) ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and T s s ∈ S is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...

Weakly mixing transformations and the Carathéodory definition of measurable sets

Amos Koeller, Rodney Nillsen, Graham Williams (2007)

Colloquium Mathematicae

Similarity:

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...

Some thoughts about Segal's ergodic theorem

Daniel W. Stroock (2010)

Colloquium Mathematicae

Similarity:

Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves. ...