Related papers: $S$-adic conjecture and Bratteli diagrams

We develop conditions for the coding of a Bratteli-Vershik system according to initial path segments to be periodic, equivalently for a constructive symbolic recursive scheme corresponding to a cutting and stacking process to produce a…

Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…

We provide characterizations of continuous eigenvalues for minimal symbolic dynamical systems described by $S$-adic structures satisfying natural mild conditions, such as recognizability and primitiveness. Under the additional assumptions…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…

In this article we prove that multidimensional effective S-adic systems, obtained by applying an effective sequence of substitutions chosen among a finite set of substitutions, are sofic subshifts.

In this note we give a detailed proof of certain results on geometry of numbers in the $S$-adic case. These results are well-known to experts, so the aim here is to provide a convenient reference for the people who need to use them.

We study the problem of improving Dirichlet's theorem of metric Diophantine approximation in the $S$-adic setting. Our approach is based on translation of the problem related to Dirichlet improvability into a dynamical one, and the main…

In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gasch\"utz. The approach follows that of P. Hauck and H. Kurtzweil for groups, by first considering complements in subalgebra…

Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange…

We prove a version of adelic descent for continuous localizing invariants.

In this paper we prove the WALA conjecture.

An idea that became unavoidable to study zero entropy symbolic dynamics is that the dynamical properties of a system induce in it a combinatorial structure. An old problem addressing this intuition is finding a structure theorem for…

A category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli's…

The goal of this paper is to put together several techniques in handling dynamical systems on zero-dimensional spaces, such as array representation, inverse limit representation, or Bratteli-Vershik representation. We describe how one can…

A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.

In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard…

We describe the structure of hyperelliptic Rauzy diagrams and hyperelliptic Rauzy-Veech groups. In particular, this provides a solution of the hyperelliptic cases of a conjecture of Zorich on the Zariski closure of Rauzy-Veech groups.

We establish a characterization of alternating links in terms of definite spanning surfaces. We apply it to obtain a new proof of Tait's conjecture that reduced alternating diagrams of the same link have the same crossing number and writhe.…

In a previous paper the second author developed a new approach to the abelian p-adic Stark Conjecture at s=1 and stated some related conjectures. This paper develops and applies techniques using p-adic measures and continued fractions to…

We give a probabilistic interpretation of the coefficients of the elementary symmetric function expansion of the chromatic quasisymmetric function for any unit interval graph. As a corollary, we prove the Stanley--Stembridge conjecture.