相关论文: Choreographies in the $n$-vortex problem

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

Iteration of the quadratic map produces sequences of polynomials whose degrees {\sl explode} as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree $4020$, while for the $52,377$ period-20…

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…

We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…

The $n+1$ vortex filament problem has explicit solutions consisting of $n$ parallel filaments of equal circulation in the form of nested polygons uniformly rotating around a central filament which has circulation of opposite sign. We show…

Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…

Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex…

This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…

We study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. We show that a spherically symmetric pulsating ball…

A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…

We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard-Balescu equations from the Klimontovich formalism. These equations take into account…

In this article we consider the motion of two bodies under the action of a Manev central force. We obtain the radius of the circular orbit and analyze its stability in sense of Lyapunov. Drawn on the first integrals of angular momentum and…

The paper investigates a generalization of the classical Sitnikov problem, concentrating on the movement of a satellite along the Z-axis as it interacts with $n$ primary bodies in periodic motion. It establishes the existence of an infinite…

The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test…

In this work, we analytically study the existence of periodic vortex cap solutions for the homogeneous and incompressible Euler equations on the rotating unit 2-sphere, which was numerically conjectured by Dritschel-Polvani and…

In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov…

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the…

For families of 4-regular directed circulant graphs with $n$ vertices, we count the number of primitive periodic orbits of length up to at least $n$. The relevant counting techniques are then extended to count the number of primitive pseudo…

In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the…