Arithmetic Results on Orbits of Linear Groups

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

The Correlation between Multiplicities of Closed Geodesics on the Modular Surface

One of the connections between Number Theory and Mathematical Physics that emerged in recent years is Arithmetical Quantum Chaos. On the physical side we have the problem of how the notion of chaos in classical dynamical systems can be transfered to quantum mechanical systems. Here Gutzwiller’s trace formula is a useful quantitative tool which connects the lengths of closed orbits in the classi...

Periodic Orbits in Arithmetical Chaos

1 Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the uncon-strained motions of particles on two dimensional surfaces of constant negative curvature whose fundamental groups are given b...

Fuzzy Sliding Mode for Spacecraft Formation Control in Eccentric Orbits

The problem of relative motion control for spacecraft formation flying in eccentric orbits is considered in this paper. Due to the presence of nonlinear dynamics and external disturbances, a robust fuzzy sliding mode controller is developed. The slopes of sliding surfaces of the conventional sliding mode controller are tuned according to error states using a fuzzy logic and reach the pre-define...

Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows

In this paper, we study the distribution of integral points on parametric families of affine homogeneous varieties. By the work of Borel and Harish-Chandra, the set of integral points on each such variety consists of finitely many orbits of arithmetic groups, and we establish an asymptotic formula (on average) for the number of the orbits indexed by their Siegel weights. Our arguments use the e...