Related papers: On generalized median triangles and tracing orbits
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
Tropicalizations form a bridge between algebraic and convex geometry. We generalize basic results from tropical geometry which are well-known for special ground fields to arbitrary non-archimedean valued fields. To achieve this, we develop…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection,…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
We construct and analyze families of periodic delay orbits for a class of delay differential equations in two dimensions depending on two real-valued functions. These families are parametrized by the delay parameter. It is possible to…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…
Any periodic trajectory on an isosceles triangle gives rise to a periodic trajectory on a right triangle obtained by identifying the halves of the original triangle. We examine the relationship between periodic trajectories on isosceles…
We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such mappings is…
The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be…
Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…
The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted…
A cosmological polytope is defined for a given Feynman diagram, and its canonical form may be used to compute the contribution of the Feynman diagram to the wavefunction of certain cosmological models. Given a subdivision of a polytope, its…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…
We discuss how triposes may be understood as generalizations of localic geometric morphisms.
The two parameter generalization of the complete elliptic integral of the second kind discussed recently by Barsan is expressed in terms of ordinary complete elliptic integrals.
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…