Suppose GR is the real points of a complex connected reductive algebraic group G defined over R. (The class of such groups is exactly the class treated by the software package atlas.) Write g R for the dual of the Lie algebra of GR and N R for the nilpotent elements in gR. Then GR acts with finitely many orbits on N via the coadjoint action, and it is clearly very desirable to parametrize these...

Currently, ultra-rapid orbits play an important role in the high-speed development of global navigation satellite system (GNSS) real-time applications. This contribution focuses on the impact of the fitting arc length of observed orbits and solar radiation pressure (SRP) on the orbit prediction performance for GPS, GLONASS, Galileo and BeiDou. One full year's precise ephemerides during 2015 wer...

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 ...

The LPA model is a three dimensional system of nonlinear difference equations that has found many applications in population dynamics and ecology. In this paper, we consider a special case of the model (a case that approximates that used in experimental bifurcation and chaos studies) and prove several theorems concerning the existence and stability of periodic cycles, invariant loops, and chaos...

We estimated the rate of comet and asteroid collisions with the terrestrial planets by calculating the orbits of 13000 Jupiter-crossing objects (JCOs) and 1300 resonant asteroids and computing the probabilities of collisions based on random-phase approximations and the orbital elements sampled with a 500 yr step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results for orbit...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

The paper presents a discussion of parameterized discrete dynamics of neural ring networks. For specific parameter domains stable periodic orbits coexist. Their periods and the number of orbits of a given period are determined. Even n-rings, i.e. rings with an even number of inhibitory connections, exhibit mainly stable period-n orbits. Odd n-rings display mainly stable period-2n orbits. The dy...

We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of f...

Recently, 3D image fusion reconstruction using a FDK algorithm along three-orthogonal circular isocentric orbits has been proposed. On the other hand, we know that 3D image reconstruction based on three-orthogonal circular isocentric orbits is sufficient in the sense of Tuy data sufficiency condition. Therefore the datum obtained from three-orthogonal circular isocentric orbits can derive an ex...

Given any K > 0, we construct two equivalent C2 flows, one of which has positive topological entropy larger than K and admits zero as the exponential growth of periodic orbits, in contrast, the other has zero topological entropy and super-exponential growth of periodic orbits. Moreover we establish a C∞ flow on S2 with super-exponential growth of periodic orbits, which is also equivalent to ano...