Related papers: Invariant critical sets of conserved quantities

We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and…

In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…

The dynamical equation satisfied by the density matrix, when a quantum system is subjected to one or more constraints arising from conserved quantities, is derived. The resulting nonlinear motion of the density matrix has the property that…

Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…

We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…

In this paper, we discuss several concepts of the modern theory of discrete integrable systems, including: - Time discretization based on the notion of B\"acklund transformation; - Symplectic realizations of multi-Hamiltonian structures; -…

We establish a dynamical version of Kuratowski-Mycielski Theorem on the existence of "large" invariant dependent sets. We apply this result to the study of invariant chaotic sets in topological dynamical systems, simplify many known results…

Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…

Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…

We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…

We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as the system approaches to the integrable…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…

We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.

A new method for the computation of conserved densities of nonlinear differential-difference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations. The algorithm, which can be…

We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First,…

Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…

The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…