Related papers: Rotated Odometers

A rotated odometer is an infinite interval exchange transformation (IET) obtained as a composition of the von Neumann-Kakutani map and a finite IET of intervals of equal length. In this paper, we consider rotated odometers for which the…

We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb Z$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a…

Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In…

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…

We study an interval exchange transformation of [0,1] formed by cutting the interval at the points 1/n and reversing the order of the intervals. We find that the transformation is periodic away from a Cantor set of Hausdorff dimension zero.…

In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a…

We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and…

In this paper we investigate translated cone exchange transformations, a new family of piecewise isometries and renormalize its first return map to a subset of its partition. As a consequence we show that the existence of an embedding of an…

We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it…

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…

We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…

We interpret the Pascal-adic transformation as a generalized induced automorphism (over odometer) and formulate the $\sigma$-finite analog of odometer which is also known as "Hajian-Kakutani transformation" (former "Ohio state example"). We…

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear…

Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of…

We develop a renormalization scheme which extends the classical Rauzy-Veech induction used to study interval exchange tranformations (IETs) and allows to study generalized interval exchange transformations (GIETs) $T: [0,1) \to [0,1)$ with…

The concept of a uniform set is introduced for an ergodic, measure-preserving transformation on a non-atomic, infinite Lebesgue space. The uniform sets exist as much as they generate the underlying $\sigma$-algebra. This leads to the result…

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…

This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…

In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given…

A Kakutani-von Neumann map is the push-forward of the group rotation (Z_2,+1) to a unit simplex via an appropriate topological quotient. The usual quotient towards the unit interval is given by the base 2 expansion of real numbers, which in…