Related papers: Cobham-Semenov theorem and $\NN^d$-subshifts
In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
If a non-periodic sequence $X$ is the image by a morphism of a fixed point of both a primitive substitution $\sigma$ and a primitive substitution $\tau$, then the dominant eigenvalues of the matrices of $\sigma$ and of $\tau$ are…
We present a new, elementary, dynamical proof of the prime number theorem.
We study the dynamics of N=1 supersymmetric systems consisting of the strongly-coupled superconformal theory T_N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as…
We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…
We give a new proof of Bogomolov's instability theorem. Furthermore we prove that it is equivalent to a statement which characterizes when the first cohomology group of a suitable divisor does not vanish.
We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results due to Guillemin and Quillen relating involutivity, restrictions, characteristics and characteristicity,…
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…
We discuss a synchronization property for subshifts, that we call $\lambda$-synchronization. Under an irreducibility assumption we associate to a $\lambda$-synchronizing subshift a simple and purely infinite $C^*$-algebra.
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a…
The concept of dynamical symmetries is specified for quantum dots under strong Coulomb blockade. It is shown that the electron cotunneling through quantum dots may be described in terms of generators of SO(n) or SU(n) dynamical groups,…
This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under…
A theorem of Cobham says that if $k$ and $\ell$ are two multiplicatively independent natural numbers then a subset of the natural numbers that is both $k$- and $\ell$-automatic is eventually periodic. A multidimensional extension was later…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We give an alternative proof of the Michael-Simon-Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension $2$.
Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map determined by any symmetry group of…