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We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present…
Using multiplicative ergodic theory we prove two formulae describing the relationships between different joint spectral radii for sets of bounded linear operators acting on a Banach space. In particular we recover a formula previously…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
For the numerical solution of the cubic nonlinear Schr\"{o}dinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to…
We compute the cyclicity of open period annuli of the following generalized Rayleigh-Li\'enard equation $$\ddot{x}+ax+bx^3-(\lambda_1+\lambda_2 x^2+\lambda_3\dot{x}^2+\lambda_4 x^4+\lambda_5\dot{x}^4+\lambda_6 x^6)\dot{x}=0$$ and the…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe…
Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics…
An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which…
Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit formula for the unique stationary measure associated to such…
Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By…
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…
This paper presents computational methods for families of linear systems depending on a parameter. Such a family is called ensemble controllable if for any family of parameter-dependent target states and any neighborhood of it there is a…
We have examined a class of Li\'enard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et…
Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…