Related papers: Dynamical systems and uniform distribution of sequ…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
New additional equations for the Newtonian dynamical systems on Riemannian manifolds are found. They supplement the previously found weak normality conditions up to the complete normality conditions for Newtonian dynamical systems.
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian) dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical sytem (or vector field) into Poincar\'e-Dulac normal form.
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…
This paper is devoted to derive some necessary and suficient conditions for the existence of positive solutions to a singular second order system of dynamic equations with Dirichlet boundary conditions. The results are obtained by employing…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori…