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One of the most common hypotheses on the theory of non-smooth dynamical systems is a regular surface as switching manifold, at which case there is at least well-defined and established Filippov dynamics. However, systems with singular…
It is shown that quantized dynamical system with second class constraints has infinite dimensional Hilbert space.
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of dominant rational self-maps, the dynamical degrees are lower…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…
It is shown that the irreversible behavior of classical systems of interacting particles is a common property for both few-body and many-body systems. It is due to the delay in the interactions between the particles. PACS: 45.50.Jf Few- and…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
Nonequilibrium steady states in driven diffusive systems exhibit many features which are surprising or counterintuitive, given our experience with equilibrium systems. We introduce the prototype model and review its unusual behavior in…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
Structure and dynamics of real nanosystems emerge from the unreduced solution of the underlying interaction problem. It has the property of dynamic multivaluedness giving genuine dynamic randomness and complexity (physics/9806002,…
It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these…
We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that: (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
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 considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present a heuristic analysis of the dynamics of general solutions to the Einstein Field Equations which highlights the possibility that such systems could possess a degree of unpredictability stronger than that which characterises…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…