Related papers: On the average principle for one-frequency systems
We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
Consider the problem of estimating the median of N items to a precision epsilon, i.e., the estimate should be such that, with a high probability, the number of items, with values both smaller than and larger than this estimate, is less than…
We investigate the effective behaviour of a small transversal perturbation of order $\epsilon$ to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic differential equation whose diffusion vector fields are…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order $\varepsilon$. An average principle is shown to hold such that the component…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version. To this end, we consider respectively, two and three quartic oscillators as the unperturbed system, and…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under…
We are concerned with averaging theorems for $\epsilon$-small stochastic perturbations of integrable equations in $\mathbb{R}^d \times \mathbb{T}^n =\{(I,\varphi)\}$ $$ \dot I(t) =0,\quad \dot \varphi(t) = \theta(I), \qquad (1)$$ and in…
Defining an error of measurement has long been a foundational problem in science: even in classical experiments, data are statistical and admit no single universally optimal definition of error. In quantum mechanics, the challenge deepens:…