2,264 research outputs found
Central limit theorems in linear dynamics
Given a bounded operator on a Banach space , we study the existence of
a probability measure on such that, for many functions , the sequence converges in distribution
to a Gaussian random variable
The multifractal box dimensions of typical measures
We compute the typical (in the sense of Baire's category theorem)
multifractal box dimensions of measures on a compact subset of .
Our results are new even in the context of box dimensions of measures
How behave the typical -dimensions of measures?
We compute, for a compact set , the value of the upper
and of the lower -dimension of a typical probability measure with support
contained in , for any . Different definitions of the
"dimension" of are involved to compute these values, following
How to Make Chance Manageable : Statistical Thinking and Cognitive Devices in Manufacturing Control
The industrial enterprise is an excellent place to view a great diversity of forms of control: control of finances and accounts, controls on the material operations of fabrication, of logistics, and control of people at every level. Managerial knowledge seeks very explicit control objectives and their study is thus particularly fruitful for one interested in the history of techniques and in the sociological aspects of control. These modes of control are embodied in often very complex plans and devices which exist, at one and the same time, as ideas (they have been conceived by humans, they are founded on certain bodies of knowledge), and in material form.
Difference sets and frequently hypercyclic weighted shifts
We solve several problems on frequently hypercyclic operators. Firstly, we
characterize frequently hypercyclic weighted shifts on ,
. Our method uses properties of the difference set of a set with
positive upper density. Secondly, we show that there exists an operator which
is -frequently hypercyclic, yet not frequently hypercyclic and that
there exists an operator which is frequently hypercyclic, yet not
distributionally chaotic. These (surprizing) counterexamples are given by
weighted shifts on . The construction of these shifts lies on the
construction of sets of positive integers whose difference sets have very
specific properties
A hypercyclic finite rank perturbation of a unitary operator
A unitary operator and a rank operator acting on a Hilbert space
\H are constructed such that is hypercyclic. This answers affirmatively
a question of Salas whether a finite rank perturbation of a hyponormal operator
can be supercyclic.Comment: published in Mathematische Annale
Common Hypercyclic Vectors for the Conjugate Class of a Hypercyclic Operator
Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense Gδ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense Gδ set. As a corollary, the hypercyclic operators on such a Banach space form a connected subset of the operator algebra with the strong operator topology
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