Gutzwiller’s semiclassical trace formula for the density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced by a modified one with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation (“ghost orbits”) can produce clear signatures in the semiclassical spectr...

We prove results towards the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of PGLn(R). After attaching to each periodic orbit an integral invariant (the discriminant) our results have the following flavour: certain standard conjectures about the distribution of such orbits hold up ...

In this paper, we present a systematic method for finding all homoclinic orbits of invertible maps in any finite dimension. One advantage of this method is that it can also be used to order and classify all the homoclinic orbits, using symbolic dynamics, if a certain criterion is satisfied. We also present a more direct scheme, which quickly locates homoclinic orbits without, however, being abl...

We studied the dynamics of the Ricker population model under perturbations by the discrete random variable e which follows distribution Pfe ˆ aig ˆ pi; i ˆ 1; . . . ; n; 0 < ai 1, n P 1. Under the perturbations, n‡ 1 blurred orbits appeared in the bifurcation diagram. Each of the n‡ 1 blurred orbits consisted of n sub-orbits. The asymptotes of the n sub-orbits in one of the n‡ 1 blurred orbits ...

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the Z2 invariant solution, with ADM mass MADM = 2MK , where MK is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic sub-manifold. The existence and radii of circular photon orbits in this sub-manifold are studied, as functions of the dista...

The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained from a finite collection of periodic orbits. In this paper, we extend these results to homoclinic and heteroclinic orbits of saddle points. These orbits are most readily computed and studied as intersections of unstable and stable manifolds comprising homoclinic or heteroclinic tangles...

A new fully numerical method is presented which employs multiple Poincaré sections to find quasi-periodic orbits. The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasi-periodic orbits and the minimal memory required to store these orbits. This meth...

The coadjoint orbits of the Virasoro group, which have been investigated by Lazutkin and Pankratova and by Segal, should according to the Kirillov-Kostant theory be related to the unitary representations of the Virasoro group. In this paper, the classification of orbits is reconsidered, with an explicit description of the possible centralizers of coadjoint orbits. The possible orbits are diff(S...

LetMg be the moduli space of genus g curves. A Hurwitz locus inMg is a locus of points representing G-covers of fixed genus g with a given ramification type. The classification of Hurwitz loci of complex curves admitting G is by the computation of orbits of a suitable surface braid group acting on the generating tuples of G. When the genus of the curve is low, the braid orbits can be enumerated...

We consider d=10 N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T8 subgroup of massless particles’ little group T8 ⋉ SO(8). For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products of T8 ⋉ SO(k1) × ...SO(kn) form, with k1 + ...kn = 8, where compact factor is sp...