In this paper we study symmetric periodic orbits of a collinear restricted three body problem, when the middle mass is the largest one. These symmetric periodic orbits are obtained from analytic continuation of symmetric periodic orbits of two collinear two body problems.

This paper completes the classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie algebras. The author has previoulsly determined such orbits for exceptional real simple Lie algebras of inner type. Here he uses the same techniques, with some modifications, to classify the admissible nilpotent orbits of E6(6) and E6(−26) under their simply connected Lie groups.

Hénon [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point particle bouncing elastically on two disks. A one parameter family of orbits, named h-orbits, was obtained by starting the particle at rest from a given height. We obtain an ...

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-JupiterOterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. More...

As the Earth revolves around the Sun, it orbits through planetary debris left from the formation of the solar system. Many of the debris objects are asteroids and comets in orbits bringing them close to the Earth and are referred to as Near-Earth-Objects (or NEOs). Of the total NEO population, some portion are in orbits actually intersecting or crossing the orbit of the Earth. The asteroids of ...

We consider strong and weak topologies on the space of orbits from the unit interval to the set of probability measures on a given domain. In particular, we are interested in periodic orbits of probability measures on the circle. We show that a real-valued rotation number can be defined in a natural way for all smooth enough orbits whose range is composed of probability measures supported on th...

Suucient conditions are found so that a family of smooth Hamiltonian ows limits to a billiard ow as a parameter ! 0. This limit is proved to be C 1 near non-singular orbits and C 0 near orbits tangent to the billiard boundary. These results are used to prove that scattering (thus ergodic) billiards with tangent periodic orbits or tangent homoclinic orbits produce nearby Hamiltonian ows with ell...

There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. The oscillating sail is a novel solar sail configuration where a triangular sail is released at a deflected angle with respect to the Sun-direction. As a result, the sail will conduct an undamped oscillating motion around the Sun-line due to th...

The aim of our study is to investigate the possibility of habitable moons orbiting the giant planet HD 23079b, a Jupitermass planet, which follows a low-eccentricity orbit in the outer region of HD 23079’s habitable zone. We show that HD 23079b is able to host habitable moons in prograde and retrograde orbits, as expected, noting that the outer stability limit for retrograde orbits is increased...

The Fibonacci cube Γn is obtained from the n-cube Qn by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube Λn is obtained. The number of vertex and edge orbits, the sets of the sizes of the orbits, and the number of orbits of each size, are determined for the Fibonacci cubes and the Lucas cubes under the...