Related papers: Dynamical models for Liouville and obstructions to…
Starting from the Riemann-Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated…
Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…
We establish a Liouville type theorem for the fractional Lane-Emden system: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=v^q&{\rm in}\,\,\R^N,\\ (-\Delta)^\alpha v=u^p&{\rm in}\,\,\R^N, \end{array} \right.…
This paper introduces a new class of observation driven dynamic models. The time evolving parameters are driven by innovations of copula form. The resulting models can be made strictly stationary and the innovation term is typically chosen…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…
We prove a Liouville type result for bounded, entire solutions to a class of variational semilinear elliptic systems, based on the growth of their potential energy over balls with growing radius. Important special cases to which our result…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…
A dynamical system is considered such that, in this system, particles move on a toroidal lattice of the dimension $N_1\times N_2$ according to a version of the rule of particle movement in Biham--Middleton--Levine traffic model. Particles…
In this paper we prove a Liouville type theorem for the stationary MHD and the stationary Hall-MHD systems. Assuming suitable growth condition at infinity for the mean oscillations for the potential functions, we show that the solutions are…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
We consider multi-particle systems with linear deterministic hamiltonian dynamics. Besides Liouville measure it has continuum of invariant tori and thus continuum of invariant measures. But if one specified particle is subjected to a simple…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…