Related papers: Dynamical generalizations of the Lagrange spectrum
The Birkhoff graph $\mathcal{B}_n$ is the Cayley graph of the symmetric group $S_n$, where two permutations are adjacent if they differ by a single cycle. Our main result is a tighter upper bound on the independence number…
Local Lorentz invariance violation can be realized by introducing extra tensor fields in the action that couple to matter. If the Lorentz violation is rotationally invariant in some frame, then it is characterized by an ``aether'', i.e. a…
We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n \geq 4$. For minimizing harmonic maps $u\in W^{1,2}(\Omega,\mathbb{S}^2)$ from $n$-dimensional domains into the two dimensional sphere we prove: (1)…
We study the so-called nonconventional averages in the context of lattice spin systems, or equivalently random colourings of the integers. For i.i.d. colourings, we prove a large deviation principle for the number of monochromatic…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
We investigate a non-axisymmetric rotating BEC in a limit of rotation frequency for which the BEC transforms into a quasi-one-dimensional system. We compute the vortex lattice wavefunction by minimizing the Gross-Pitaevskii energy…
The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that…
The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic version of de-Sitter symmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class of accelerations linear in time. We study…
A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. We derive in this paper some upper bounds to the size of the limit set. This improves results…
The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element.…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
We show that if the complexity difference function p(n+1)-p(n) of a infinite minimal shift is bounded, then the the automorphism group of the one-sided shift is finite, and the automorphism group of the corresponding two-sided shift "modulo…
Let $K_n$ denote the set of all nonsingular $n\times n$ lower triangular $(0,1)$-matrices. Hong and Loewy (2004) introduced the number sequence $$ c_n=\min\{\lambda\mid\lambda~\text{is an eigenvalue of}~XX^{\rm T},~X\in K_n\},\quad…
In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kinetic Boltzmann equations and the kinetic wave equations, in…
The Arnoux-Rauzy systems are defined in \cite{ar}, both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. Novikov, we investigate the dynamical properties of the…