Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space dynamics in their neighborhood. We provide a pedestrian presentation of this classical theory and extend it by including systematically the periodic orbits lying in the complex plane on each side of the bifurcation. This allows for a more coherent and unified treatment of contributions of periodic orbits in semiclassical expansions. The contribution of complex fixed points is find to be exponentially small only for a particular type of bifurcation (the extremal one). In all other cases complex orbits give rise to corrections in powers of $\hbar$ and, unlike the former one, their contribution is hidden in the ``shadow'' of a real periodic orbit.Comment: better ps figures available at http://www.phys.univ-tours.fr/~mouchet or on request to [email protected]

X-ray Variability of AGN and the Flare Model

Short-term variability of X-ray continuum spectra has been reported for several Active Galactic Nuclei. Significant X-ray flux variations are observed within time scales down to 10^3-10^5 seconds. We discuss short variability time scales in the frame of the X-ray flare model, which assumes the release of a large hard X-ray flux above a small portion of the accretion disk. The resulting observed X-ray spectrum is composed of the primary radiation and of a reprocessed Compton reflection component that we model with numerical radiative transfer simulations. The incident hard X-rays of the flare will heat up the atmosphere of the accretion disk and hence induce thermal expansion. Eventually, the flare source will be surrounded by an optically thick medium, which should modify the observed spectra.Comment: 4 pages, 3 figures, accepted proceedings for a talk at the conference "AGN variability from the X-rays to the radio", June 2004, Crimean Observator

Iron lines from transient and persisting hot spots on AGN accretion disks

[abridged] We model the X-ray reprocessing from a strong co-rotating flare above an accretion disk in active galactic nuclei. We explore the horizontal structure and evolution of the underlying hot spot. To obtain the spectral evolution seen by a distant observer, we apply a general relativity ray-tracing technique. We concentrate on the energy band around the iron K-line, where the relativistic effects are most pronounced. Persistent flares lasting for a significant fraction of the orbital time scale and short, transient flares are considered. In our time-resolved analysis, the spectra recorded by a distant observer depend on the position of the flare/spot with respect to the central black hole. If the flare duration significantly exceeds the light travel time across the spot, then the spot horizontal stratification is unimportant. On the other hand, if the flare duration is comparable to the light travel time across the spot radius, the lightcurves exhibit a typical asymmetry in their time profiles. The sequence of dynamical spectra proceeds from more strongly to less strongly ionized re-emission. At all locations within the spot the spectral intensity increases towards edge-on emission angles, revealing the limb brightening effect. Future X-ray observatories with significantly larger effective collecting areas will enable to spectroscopically map out the azimuthal irradiation structure of the accretion disk and to localize persistent flares. If the hot spot is not located too close to the marginally stable orbit of the black hole, it will be possible to probe the reflecting medium via the sub-structure of the iron K-line. Indications for transient flares will only be obtained from analyzing the observed lightcurves on the gravitational time scale of the accreting supermassive black hole.Comment: 15 pages, 8 figures, accepted by Astronomy & Astrophysic

High prevalence of giardiasis in an urban population in Niger

Un échantillon de 2569 personnes (1190 hommes et 1379 femmes) provenant de la ville de Niamey (329.000 habitants), capitale du Niger, s'est révélé atteint de giardiase avec une prévalence de 28,5 %. Cette prévalence est identique chez les hommes et les femmes et atteint surtout le groupe d'âge des 3 à 29 an

The puzzle of the soft X-ray excess in AGN: absorption or reflection?

The 2-10 keV continuum of AGN is generally well represented by a single power law. However, at smaller energies the continuum displays an excess with respect to the extrapolation of this power law, called the ''soft X-ray excess''. Until now this soft X-ray excess was attributed, either to reflection of the hard X-ray source by the accretion disk, or to the presence of an additional comptonizing medium, giving a steep spectrum. An alternative solution proposed by Gierlinski and Done (2004) is that a single power law well represents both the soft and the hard X-ray emission and the impression of the soft X-ray excess is due to absorption of a primary power law by a relativistic wind. We examine the advantages and drawbacks of reflection versus absorption models, and we conclude that the observed spectra can be well modeled, either by absorption (for a strong excess), or by reflection (for a weak excess). However the physical conditions required by the absorption models do not seem very realistic: we would prefer an ''hybrid model''.Comment: 4 pages, 3 figures, abstracts SF2A-2005, published by EDP-Sciences Conference Serie

Floquet Analysis of Atom Optics Tunneling Experiments

Dynamical tunneling has been observed in atom optics experiments by two groups. We show that the experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The observed tunneling has a well defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate. We find frequencies which match those observed in both experiments. The dynamical origin of the dominant Floquet states is identified.Comment: Accepted in Physical Review