Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form lω1 +mω2 + nω3 = 0 between the three fundamental frequencies. Boxlets are special cases of resonant orbits in which one of the integers (l,m, n) is zero. Resonant orbits are confined for all time to a membrane in configuration space; they play roug...

We study bifurcations from one-parameter families of symmetric periodic orbits in reversible systems and give simple criteria for subharmonic symmetric periodic orbits to be born from the one-parameter families. Our result is illustrated for a generalization of the Hénon-Heiles system. In particular, it is shown that there exist infinitely many families of symmetric periodic orbits bifurcating ...

Question. Does system (1.1) have periodic orbits when system (1.2) has periodic orbits? Recently, there have been a lot of researches in the literature on the periodicity of discrete-time dynamical systems [1, 3–8, 10, 11]. However, to the authors’ knowledge the above question has not received investigations, therefore in this paper we study the above question and obtain a fundamental result. O...

Let P+(n) be the Siegel parabolic subgroup of O(n, n), and P−(n) be the Siegel parabolic subgroup of Sp2n(R). In this paper, we study the coadjoint orbits of P±(n). We establish a one-to-one correspondence between the real coadjoint orbits of Sp2n(R) and the principal coadjoint orbits of P+(2n), and a one-to-one correspondence between the real coadjoint orbits of O(p, n− p) with p ∈ [0, n] and ...

OBJECTIVE To compare superior ophthalmic vein blood flow parameters measured with color Doppler imaging in patients with congestive Graves' orbitopathy before and after treatment and in normal controls. METHODS Twenty-two orbits from 12 patients with Graves' orbitopathy in the congestive stage and 32 orbits from 16 normal controls underwent color Doppler imaging studies. Color Doppler imaging...

Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is the existence problem for regular compact energy levels without periodic orbits. Very little is known about how large the set of regular energy values witho...

In this article we describe the coadjoint orbits of SL(2,R). After choosing polarizations for each orbits, we pointed out the corresponding quantum coadjoint orbits and therefore unitary representations of SL(2,R) via deformation quantization.

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits, which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension 1. Several bifurcation scenarios are described in detail. They are ...

The shape of a galaxy is constrained both by mechanisms of formation (dissipational vs. dissipationless) and by the available orbit families (the shape and amount of regular and stochastic orbits). It is shown that, despite the often very flattened shapes of banana and fish orbits, these boxlet orbits generally do not fit a triaxial galaxy in detail because, similar to loop orbits, they spend t...

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits' geome...