Related papers: Stationary phase type estimates for low symbol reg…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
We use the stationary phase method to determine the path of optical beams which propagate through a dielectric block. In the presence of partial internal reflection, we recover the geometrical result obtained by using the Snell law. For…
Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov…
We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
In this paper, we shall prove the $L^{p}$ endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases $S$ in $\mathbb{R} \times \mathbb{R}$. As a consequence, sharp $L^{p}$ decay estimates are also obtained…
We obtain integral boundary decay estimates for solutions of fourth-order elliptic equations on a bounded domain with regular boundary. We apply these estimates to obtain stability bounds for the corresponding eigenvalues under small…
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
In this note, we generalize the Fresnel integrals using oscillatory integral, and then we obtain an extention of the stationary phase method.
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean…
In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard one-dimensional van der Corput lemma with the…
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…
In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…
In applying the stationary phase approximation to coherent state path integrals a difficulty occurs; there are no classical paths that satisfy the boundary conditions of the path integral. Others have gotten around this problem by…