相关论文: Perturbed Three Vortex Dynamics

We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…

Recent studies of pseudo-plane ideal flow (PIF) reveal a ubiquitous presence of vortex alignment in both homogeneous and stratified fluids, and in both inertial and rotating reference frames as well. The exact solutions of a steady-state…

Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in $U \subset \mathbb{R}^n$ to a planar harmonic oscillator defined on the symplectic…

We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on…

We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…

Existence of a stationary mode for a Hamiltonian dynamic system of two point vortexes with different signs on different latitudes of a uniform rotating sphere complying with observed data is stated. It is shown that such mode realization is…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable with the Hamiltonian and the genralized total momentum being two integrals of motion. The model in…

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…

We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges. We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear…

This study examines the motion of spherical inertial particles in a three-dimensional rotating cylindrical vortex - a simplified model of geophysical flow structures such as oceanic eddies. The analytical vortex formulation enables the…

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2,…

We prove the existence of real analytic Hamiltonians with topologically unstable quasi-periodic invariant tori. Using various versions of our examples, we solve the following problems in the stability theory of analytic quasi-periodic…

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an…

Admissible perturbations (i.e., perturbations that do not change the Mironenko reflecting function of the system) are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained…

It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…

In this work the stability of perturbed linear time-varying systems is studied. The main features of the problem are threefold. Firstly, the time-varying dynamics is not required to be continuous but allowed to have jumps. Also the system…

In this paper the problem of persistence of invariant tori under small perturbations of integrable Hamiltonian systems is considered. The existence of one-to-one correspondence between hyperbolic invariant tori and critical points of the…

Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…

We investigate the collective dynamics of multivortex assemblies in a two dimensional (2D) toroidal fluid film of distinct curvature and topology. The incompressible and inviscid nature of the fluid allows a Hamiltonian description of the…