Related papers: Periodic orbits of the Stark problem
We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, we find some disk-like global surfaces of section with…
In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…
In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass-radius relations, moments of…
We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical…
We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary…
In this paper we prove the existence of non-stationary periodic solutions of delay Lotka-Volterra equations. In the proofs we use the degree for $S^1$-equivariant maps.
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
This article is devoted to stationary solutions of Euler's equation on a rotating sphere, and to their relevance to the dynamics of stratospheric flows in the atmosphere of the outer planets of our solar system and in polar regions of the…
We give a necessary and sufficient condition for strong stability of low dimensional Hamiltonian systems, in terms of the iterates of a closed orbit and the Conley-Zehnder index. Applications to Mathieu equation and stable harmonic…
Tidal disruptions of stars on the equatorial plane orbiting Kerr black holes have been widely studied. However thus far, there have been fewer studies of stars in inclined precessing orbits around a Kerr black hole. In this paper, we use…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…
It is shown that for very rapidly rotating low mass strange stars the marginally stable orbit is located above the stellar surface. This effect is explained by the very important role of the oblateness of the rotating strange star. The…
In this paper, we establish the existence and stability properties of odd periodic waves related to the Klein-Gordon type equations, which include the well known $\phi^4$ and $\phi^6$ models. Existence of periodic waves is determined by…
We study the geodesic motion of massless particles in singly rotating black ring spacetimes. We find stable stationary orbits of massless particles in toroidal spiral shape in the case that the thickness parameter of a black ring is less…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
In this article, we investigate the motion of a spinning particle at a constant inclination, different from the equatorial plane, around a Kerr black hole. We mainly explore the possibilities of stable circular orbits for different spin…
The influence of the irregular forces on the evolution of a triple hierarchical stellar system moving in the field of stars have been studied. Triple hierarchical stellar systems are stable in contrary to the stellar systems with comparable…
The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three…