Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs

In this paper, we deal with a classical object, namely, a nonhyperbolic limit cycle in a system of smooth autonomous ordinary differential equations. While the existence of a center manifold near such a cycle was assumed in several studies on cycle bifurcations based on periodic normal forms, no proofs were available in the literature until recently. The main goal of this paper is to give an elementary proof of the existence of a periodic smooth locally invariant center manifold near a nonhyperbolic cycle in finite-dimensional ordinary differential equations by using the Lyapunov-Perron method. In addition, we provide several explicit examples of analytic vector fields admitting (non)-unique, (non)-$C^{\infty}$-smooth and (non)-analytic periodic center manifolds.Comment: 35 pages, 4 figure

Spin structure function g_1 at low x: status and plans

A brief review of measurements and expectations concerning the spin structure function g_1 of the nucleon at low values of the scaling variable x is given.Comment: 4 pages, 3 figures. Invited talk presented at the ``International Workshop on the Spin Structure of the Proton and Polarized Collider Physics'', ECT*, Trento, Italy, July 23-28, 200

Review of recent results in spin physics

Recent results in polarized DIS are reviewed. Particular emphasis is placed on new measurements of transverse and longitudinal asymmetries, on the tests of the spin sum rules and on the analysis of the spin structure function $g_1$ in perturbative QCD at NLO.Comment: 15 pages, LaTex, 15 eps figures included, to be published in Proceedings of 7th Int. Workshop on Deep Inelastic Scattering and QCD (DIS99

Mapping the x dependence of the axial anomaly in polarised deep inelastic scattering

We discuss the role of the U(1) axial anomaly in the spin structure functions of the nucleon, with particular emphasis on how one might determine its x dependence in present and future deep inelastic scattering experiments. We focus on the C-odd spin structure function g3 and also the deuteron structure function g1^d.Comment: 11pages Latex, 6 Figs. appended as .ps files after main text, Cavendish preprint HEP-93/

The Strange Quark Polarisation from Charged Kaon Production on Deuterons

The strange quark helicity distribution Delta s(x)is derived at LO from the semi-inclusive and inclusive spin asymmetries measured by the COMPASS experiment at CERN. The significance of the results is found to depend critically on the ratio of the sbar and u quark fragmentation functions into positive kaons.Comment: 4 pages, 3 figures, Proceedings of the XVIIIth Symposium on Spin Physics, Charlottesville (Virginia, USA), October 6-11,200

Gauge symmetry and the EMC spin effect

We emphasise the EMC spin effect as a problem of symmetry and discuss the renormalisation of the $C=+1$ axial tensor operators. This involves the generalisation of the Adler-Bell-Jackiw anomaly to each of these operators. We find that the contribution of the axial anomaly to the spin dependent structure function $g_1 (x, Q^2)$ scales at $O(\alpha_s)$. This means that the anomaly can be a large $x$ effect in $g_1$. Finally we discuss the jet signature of the anomaly.Comment: 17 pages, Latex, Cavendish preprint HEP 93/

A Bound on the Energy Loss of Partons in Nuclei

We derive a quantum mechanical upper bound on the amount of radiative energy loss suffered by high energy quarks and gluons in nuclear matter. The bound shows that the nuclear suppression observed in quarkonium production at high $x_F$ cannot be explained in terms of energy loss of the initial or final parton states. We also argue that no nuclear suppression is expected in the photoproduction of light hadrons at large $x_F$.Comment: 15 pages, 1 figure included as a Postscript file, phyzzx.te

Transverse Momentum in Semi-Inclusive Polarized Deep Inelastic Scattering and the Spin-Flavor Structure of the Proton

The non-valence spin-flavor structure of the nucleon extracted from semi-inclusive measurements of polarized deep inelastic scattering depends strongly on the transverse momentum of the detected hadrons which are used to determine the individual polarized sea distributions. This physics may explain the recent HERMES observation of a positively polarized strange sea through semi-inclusive scattering, in contrast to the negative strange sea polarization deduced from inclusive polarized deep inelastic scattering.Comment: 4 pages, revtex style, 2 figure