Related papers: Singular substitutions of constant length

We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…

We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We investigate whether certain spectral phenomena are generic…

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…

In this paper an asymptotic formula is given for the Lebesgue constants generated by the anisotropically dilated $d$-dimensional simplex. Contrary to many preceding results established only in dimension two, the obtained ones are proved in…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the…

The Maxwell-Dirac equations are the equations for electronic matter, the "classical" theory underlying QED. In this article we examine the stationary Maxwell-Dirac equations under weak regularity and decay assumptions. We prove that: There…

A method of confirming the absence of absolutely continuous diffraction via the positivity of Lyapunov exponents derived from the corresponding Fourier matrices is presented, which provides an approach that is independent of previous…

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…

We give an in depth analysis of the subwords of the Thue-Morse sequence. This allows us to prove that there are infinitely many injective primitive substitutions with Perron-Frobenius eigenvalue 2 that generate a symbolic dynamical system…

In this article, we establish the Picard-Lindelof theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution. The proof is produced by using convergence…

We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of…

The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…

We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an…

In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…

We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…

In this note we give an example of an ergodic non-singular map whose unitary operator admits a Lebesgue component of multiplicity one in its spectrum.

The energy spectrum of a system containing a static quark anti-quark pair is computed for a wide range of source separations using lattice QCD with $N_\mathrm{f}=2+1$ dynamical flavours. By employing a variational method with a basis…

We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independent of the perturbation, the residual spectrum is empty, and…

In this paper we construct a q-analogue of the Legendre transformation, where q is a matrix of formal variables defining the phase space braidings between the coordinates and momenta (the extensive and intensive thermodynamic observables).…