Related papers: Singularities of invariant densities for random sw…

Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…

We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…

In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…

Newtonian, undamped motion in single-well potentials belong to a class of well-studied conservative systems. Here, we investigate and compare long-time properties of fully deterministic motions in single-well potentials with analogous…

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…

In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…

This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…

The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular…

We study the singularities of the projective dual variety.

All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…

In the present paper, we theoretically study the effect of density of state variation on the phenomena in the discontinuous magnetic field. Special attention is paid to the transient processes when the magnetic field is switched on (off).…

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous…

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…

The objective of this paper is to discuss invariants of singularities of algebraic schemes over fields of positive characteristic, and to show how they yield the simplification of singularities. We focus here on invariants which arise in an…

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…