Related papers: Kepler motion on single-sheet hyperboloid
We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the energy surface is equivalent to a Reeb flow on the tight…
The first result of this paper is that every contact form on $\mathbb{R} P^3$ sufficiently $C^\infty$-close to a dynamically convex contact form admits an elliptic-parabolic closed Reeb orbit which is $2$-unknotted, has self-linking number…
The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never stressed enough in the physical or mathematical literature…
In this paper we study two electrons on a line on the same side of the nucleus which interact with each other by their mean value. We prove that there exists a unique periodic orbit and examine for which charges the two orbits of the…
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form…
We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
We study the contact geometry of the connected components of the energy hypersurface, in the symmetric restricted 3-body problem on $\mathbb{S}^2$, for a specific type of motion of the primaries. In particular, we show that these components…
We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit $(t,x)\to (t/\eps,x/\eps)$. We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the…
We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…
A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a…
We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy…
In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…
We introduce the regularization Levi-Civita parameter for the `curved Kepler', i.e., motion under the `Kepler-Coulomb' potential in a configuration space with any constant curvature and metric of any signature type. Consistent use of this…
Motivated by a certain type of unfolding of a Hopf-Hopf singularity, we consider a one-parameter family $(f_\gamma)_{\gamma\geq0}$ of $C^3$--vector fields in $\mathbb{R}^4$ whose flows exhibit a heteroclinic cycle associated to two periodic…
We present an algorithm for constructing analytically approximate integrals of motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a…
We consider perturbations of the diffusive Hamilton-Jacobi equation \begin{equation*} %\label{non_pert} \left\{ \begin{array}{lcl} \hfill -\Delta u &=& (1+g(x))| \nabla u|^p\qquad \mbox{ in } \IR^N_+, \\ \hfill u &=& 0 \hfill \mbox{ on }…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
The existence of parabolic orbits is obtained for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of non-collision periodic solutions which are obtained by Mountain Pass Lemma.