Related papers: Stability of Skorokhod problem is undecidable
The present paper is devoted to a systematic study of the $p$-Brownian convergence introduced in \cite{boudabra2026stability} (in press) to study the stability of the planar Skorokhod embedding problem \cite{gross2019,Boudabra2020}. The…
The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains,…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to…
The \emph{Skorokhod distance} is a natural metric on traces of continuous and hybrid systems. For two traces, from $[0,T]$ to values in a metric space $O$, it measures the best match between the traces when allowed continuous bijective…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
A system of Brownian hard balls is regarded as a reflecting Brownian motion in the configuration space and can be represented by a solution to a Skorohod-type equation. In this article, we consider the case that there are an infinite number…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…
Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by…
Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…
We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate…