Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.Comment: 12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chao

Disc galaxies with multiple triaxial structures. II. JHK surface photometry and numerical simulations

We present detailed JHK surface photometry with ellipse fits of 13 galaxies selected from previous optical observations as likely candidates for having a secondary bar or a triaxial bulge within the primary bar. We have found 7 double-barred galaxies, 3 double-barred galaxies with an additional intermediate structure with twisted isophotes, and 3 galaxies with a bar and central twisted isophotes. A global analysis of the structural parameter characteristics in the I- and K-bands is presented. Various numerical models of galaxies with bars within bars are also analysed using the ellipse fitting technique and compared to the observations. A thorough review of the possible hypotheses able to explain this phenomenon is given with emphasis on the most likely ones.Comment: 12 pages, AATEX. Accepted for publication in A&A. Large color postscript figures omitted (Figs. 1), figures 2-9 included; gzip'ed postscript files of the paper and Figs. 1 available via anonymous ftp at ftp://obsftp.unige.ch/pub/fri/aasjhk/ , files fri_aasjhk.ps.gz and ngc*.ps.g

Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chao

Bibliographie commentée sur le patrimoine culturel immatériel

Cette bibliographie a été établie pour accompagner l’étude de droit comparé menée dans le cadre du projet Osmose. Cette étude de droit comparé s’attachant à l’articulation entre le droit international et le droit interne, la structure de la bibliographie reprend ces deux plans d’analyse. Elle est par conséquent divisée en deux blocs principaux : l’un consacré au patrimoine culturel immatériel en droit international et l’autre au patrimoine culturel immatériel en droit interne