Related papers: On Chouikha's isochronicity criterion

The conventional nature of synchronisation is discussed in inertial frames, where it is found that theories using different synchronisations are experimentally equivalent to special relativity. In contrary, in accelerated systems only a…

General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and…

The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…

We use Sigma-invariants to study homotopical and homological finiteness properties of fixed subgroups of automorphisms of a group $G$ in terms of its center $Z(G)$ and the induced automorphisms on its associated quotient $G/Z(G)$.…

Chaplygin proved the integrability by quadratures of a round sphere, rolling without slipping on a horizontal plane, with center of mass at the center of the sphere, but with arbitrary moments of inertia. Although the system is integrable…

We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a…

This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…

An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.

In this paper, we study a positive characteristic analogue of the centers of log canonicity of a pair $(R, \Delta)$. We call these analogues centers of $F$-purity. We prove positive characteristic analogues of subadjunction-like results,…

We study pointwise behavior of positive solutions to nonlinear integral equations, and related inequalities, of the type \begin{equation*} u(x) - \int_\Omega G(x, y) \, g(u(y)) d \sigma (y) = h, \end{equation*} where $(\Omega, \sigma)$ is a…

We show how the condition of isochronicity can be studied for two dimensional systems in the renormalization group (RG) context. We find a necessary condition for the isochronicity of the Cherkas and another class of cubic systems. Our…

We investigate the continuity properties of the homogenized boundary data $\overline{g}$ for oscillating Dirichlet boundary data problems. We show that, for a generic non-rotation-invariant operator and boundary data, $\overline{g}$ is…

Let G:=-((d/dx)^2+x^2(d/du)^2) denote the Grusin operator on R^2. Consider the Cauchy problem for the associated wave equation on R x R^2, given by ((d/dt)^2+G)v =0, v(0,.)=f, d/dt v(0,.)=g, where t denotes time and f, g are suitable…

We study the synchronization properties of the random double rotations on tori. We give a criterion that show when synchronization is present in the case of random double rotations on the circle and prove that it is always absent in…

In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system $\ddot q(t)=-\nabla U(q(t))$ in the presence of symmetries of a compact Lie group $\Gamma$ acting…

We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups $X/G$ in the setting of derived loop spaces as well as Hochschild homology and its cyclic…

We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young's estimates on towers are always optimal. Moreover, we show…

Formulae for the value of a harmonic function at the center of a rectangle are found that involve boundary integrals. The central value of a harmonic function is shown to be well approximated by the mean value of the function on the…

This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \dot{x} = y, \quad \dot{y} = -\alpha y - \epsilon x^m - \sigma x, $$ where $\epsilon \neq…

The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the…