Related papers: Oscillating sequences, Gowers norms and Sarnak's c…

Orientable sequences of order n are infinite periodic sequences with symbols drawn from a finite alphabet of size k with the property that any particular subsequence of length n occurs at most once in a period in either direction. They were…

We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to a flow on a solid torus, with at most a finite number of…

We investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…

The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath…

Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…

We prove that strongly $b$-multiplicative functions of modulus $1$ along squares are asymptotically orthogonal to the M\"obius function. This provides examples of sequences having maximal entropy and satisfying this property.

We consider a $C^{1,\alpha}$ smooth flow in $\mathbb{R}^n$ which is "strongly monotone" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We…

An asymptotically orthonormal sequence is a sequence which is 'nearly' orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized…

We consider topological dynamical systems given by skew products $S\rtimes_{\tau} T$, where $S\colon Y\to Y$ is a subshift, $\tau\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For…

In this paper we have considered higher order two dimensional coupled system of non-linear ordinary differential equations. We have given necessary and sufficient conditions on the non-linear functions such that the solutions pair oscilla

In the Horndeski's most general scalar-tensor theories, we derive the three-point correlation function of scalar non-Gaussianities generated during single-field inflation in the presence of slow-variation corrections to the leading-order…

In this paper, we study the irregular set of any continuous observable for a class of skew product transformations, which is driven by a uniquely ergodic homeomorphism system $(\Omega,\mathbb{P},\theta)$ and satisfies Anosov and toplogical…

We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective…

Odd viscosity is a transport coefficient that can occur when fluids experience breaking of parity and time-reversal symmetry. Previous knowledge indicates that cylinders in incompressible odd viscous fluids, under no-slip boundary…

The dissipation--coherence bound is a conjectured tradeoff between entropy production and the quality of stochastic oscillations. We show that this tradeoff follows from the higher-order thermodynamic uncertainty relation together with a…

We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…

Caucal hierarchy is a well-known class of graphs with decidable monadic theories. It were proved by L. Braud and A. Carayol that well-orderings in the hierarchy are the well-orderings with order types less than $\varepsilon_0$. Naturally,…

We study the asymptotic behavior of the sequence $\{\Omega(n) \}_{ n \in \mathbb{N} }$ from a dynamical point of view, where $\Omega(n)$ denotes the number of prime factors of $n$ counted with multiplicity. First, we show that for any…

We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…

We produce explicit low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a convex domain with positive curvature in R^2. The proof depends on simultaneous diophantine…