相关论文: A geometrical method towards first integrals for d…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
In the phase space of the integrable Hamiltonian system with three degrees of freedom used to describe the motion of a Kowalevski-type top in a double constant force field, we point out the four-dimensional invariant manifold. It is shown…
In this paper we try to establish a connection between a three-dimensional Lotka--Volterra dynamical system and two-dimensional topological surgery. There are many physical phenomena exhibiting two-dimensional topological surgery through a…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
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,…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
Numerical approximations of two classical fluid dynamics systems modelling large structure formation in cosmology are proposed. These systems model nonrelativistic and relativistic fluids submitted to self-gravitation in an expanding…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the…
We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto…
The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…
We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in…
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the standard brute force experiments can be…
We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
Consider a general $3$-dimensional Lotka-Volterra system with a rational first integral of degree two of the form $H=x^i y^j z^k$. The restriction of this Lotka-Volterra system to each surface $H(x,y,z)=h$ varying $h\in \mathbb{R}$ provide…
We consider autonomous holonomic dynamical systems defined by equations of the form $\ddot{q}^{a}=-\Gamma_{bc}^{a}(q) \dot{q}^{b}\dot{q}^{c}$ $-Q^{a}(q)$, where $\Gamma^{a}_{bc}(q)$ are the coefficients of a symmetric (possibly…