Approach to a rational rotation number in a piecewise isometric system

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain with vanishing measure; this map is the product of two involutions, and each involution preserves all its atoms. Dynamically, the composition of these involutions represents linking together two sector maps; this dynamical system features an orderly array of stable periodic orbits having a smooth parameter dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

DIRAC Experiment and Test of Low-Energy QCD

The low-energy QCD predictions to be tested by the DIRAC experiment are revised. The experimental method, the setup characteristics and capabilities, along with first experimental results are reported. Preliminary analysis shows good detector performance: alignment error via $\Lambda$ mass measurement $m_\Lambda = 1115.6 MeV/c^2$ with $\sigma = 0.92 MeV/c^2$, $p \pi^-$ relative momentum resolution $\sigma_Q \approx 2.7 MeV/c$, and evidence for $\pi^

Detection of Pionium with DIRAC

The aim of the DIRAC experiment at CERN is to provide an accurate determination of S-wave pion-pion scattering lengths from the measurement of the lifetime of the pi+ pi- atom. The measurement will be done with precision comparable to the level of accuracy of theoretical predictions, formulated in the context of Chiral Perturbation Theory. Therefore, the understanding of chiral symmetry breaking of QCD will be submitted to a stringent test

Dirac experiment

The main objective of DIRAC experiment is the measurement of the lifetime tau of the exotic hadronic atom consisting of pi /sup +/ and pi /sup -/ mesons. The lifetime of this atom is determined by the decay mode pi /sup +/ pi /sup -/ to pi /sup 0/ pi /sup 0/ due to the strong interaction. Through the precise relationship between the lifetime and the S-wave pion-pion scattering length difference a/sub 0/-a/sub 2/ for isospin 0 and 2 (respectively), a measurement of tau with an accuracy of 10% will allow a determination of a/sub 0/-a/sub 2/at a 5% precision level. Pion-pion scattering lengths have been calculated in the framework of chiral perturbation theory with an accuracy below 5%. In this way DIRAC experiment will provide a crucial test of the chiral symmetry breaking scheme in QCD effective theories at low energies. (19 refs)