1,818 research outputs found
Cocycles over interval exchange transformations and multivalued Hamiltonian flows
We consider interval exchange transformations of periodic type and construct
different classes of recurrent ergodic cocycles of dimension over this
special class of IETs. Then using Poincar\'e sections we apply this
construction to obtain recurrence and ergodicity for some smooth flows on
non-compact manifolds which are extensions of multivalued Hamiltonian flows on
compact surfaces.Comment: 45 pages, 2 figure
Remarks on step cocycles over rotations, centralizers and coboundaries
By using a cocycle generated by the step function over an irrational rotation , we present examples which illustrate different aspects
of the general theory of cylinder maps. In particular, we construct non ergodic
cocycles with ergodic compact quotients, cocycles generating an extension
with a small centralizer. The constructions are related
to diophantine properties of
Centralizer and liftable centralizer of special flows over rotations
The liftable centralizer for special flows over irrational rotations is
studied. It is shown that there are such flows under piecewise constant roof
functions which are rigid and whose liftable centralizer is trivial
On multiple ergodicity of affine cocycles over irrational rotations
Let T_\alpha denote the rotation T_{\alpha}x=x+\alpha (mod 1) by an
irrational number \alpha on the additive circle T=[0,1). Let \beta_1,...,
\beta_d be d\geqslant 1 parameters in [0, 1). One of the goals of this paper is
to describe the ergodic properties of the cocycle (taking values in R^(d+1))
generated over T_\alpha by the vectorial function \Psi_{d+1}(x):=(\phi(x),
\phi(x+\beta_1),..., \phi(x+\beta_d)), with \phi(x)={x}-1/2.
It was already proved in \cite{LeMeNa03} that \Psi_{2} is regular for \alpha
with bounded partial quotients. In the present paper we show that \Psi_{2} is
regular for any irrational \alpha. For higher dimensions, we give sufficient
conditions for regularity. While the case d=2 remains unsolved, for d=3 we
provide examples of non-regular cocycles \Psi_{4} for certain values of the
parameters \beta_1,\beta_2,\beta_3.
We also show that the problem of regularity for the cocycle \Psi_{d+1}
reduces to the regularity of the cocycles of the form \Phi_{d} =(1_{[0,
\beta_j]} - \beta_j)_{j= 1, ..., d} (taking values in R^d). Therefore, a large
part of the paper is devoted to the classification problems of step functions
with values in R^{d}.Comment: 34 pages; revisions in response to referees' comment
Limit law for some modified ergodic sums
An example due to Erdos and Fortet shows that, for a lacunary sequence of
integers (q_n) and a trigonometric polynomial f, the asymptotic distribution of
normalized sums of f(q_k x) can be a mixture of gaussian laws. Here we give a
generalization of their example interpreted as the limiting behavior of some
modified ergodic sums in the framework of dynamical systems
Drilling Information System (DIS) and Core Scanner
The Drilling Information System is a modular structure of databases, tailored user applications as well as web services and instruments including appropriate interfaces to DIS. This tool set has been developed for geoscientific drilling projects but is applicable to other distributed scientific operations. The main focuses are the data acquisition on drill sites (ExpeditionDIS), and the curation of sample material e.g., in core repositories (CurationDIS). Due to the heterogeneity of scientific drilling projects, a project-specific DIS is arranged and adjusted from a collection of existing templates and modules according to the user requirements during a one week training course. The collected data are provided to the Science Team of the drilling project by secured Web services, and stored in long-term archives hosted at GFZ. At the end the data sets and sample material are documented in an Operational Report (e.g., Lorenz et al., 2015) and published with assigned DOI (Digital Object Identifier) and IGSN (International Geo Sample Number; for physical samples) by GFZ Data Services
Ergodicity for Infinite Periodic Translation Surfaces
For a Z-cover of a translation surface, which is a lattice surface, and which
admits infinite strips, we prove that almost every direction for the
straightline flow is ergodic
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