Periodic motions galore: How to modify nonlinear evolution equations so that they feature a lot of periodic solutions

A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.Comment: arxiv version is already officia

Algebraically Linearizable Dynamical Systems

The main result of this paper is the evidence of an explicit linearization of dynamical systems of Ruijsenaars-Schneider type and of the perturbations introduced by F. Calogero of these systems with all orbits periodic of same period. Several other systems share the existence of this explicit linearization, among them, the Calogero-Moser system (with and without external potential) and the Calogero-Sutherland system. This explicit linearization is compared with the notion of maximal superintegrability which has been discussed in several articles.Comment: 11 pages, Late

Lopsided Spiral Galaxies

The light distribution in the disks of many galaxies is non-axisymmetric or `lopsided' with a spatial extent much larger along one half of a galaxy than the other, as in M101. Recent near-IR observations show that lopsidedness is common. The stellar disks in nearly 30 % of galaxies have significant lopsidedness, greater than 10 % measured as the Fourier amplitude of the m=1 component normalized to the average value. This asymmetry is traced particularly well by the atomic hydrogen gas distribution lying in the outer parts. The lopsidedness also occurs in the nuclear regions, where the nucleus is offset with respect to the outer isophotes. The galaxies in a group environment show higher lopsidedness. The origin of lopsidedness could be due to the disk response to a tidally distorted halo, or via gas accretion. The lopsidedness has a large impact on the dynamics of the galaxy, its evolution, the star formation in it, and on the growth of the central black hole and on the nuclear fueling, merging of binary black holes etc. The disk lopsidedness can be used as a diagnostic to study the halo asymmetry. This is an emerging area in galactic structure and dynamics. In this review, the observations to measure the lopsided distribution, as well as the theoretical progress made so far to understand its origin and properties, and the related open problems will be discussed. (abridged).Comment: 75 pages, 28 figures, a review article, to be published by Physics Report

Near-IR photometry of disk galaxies: search for nuclear isophotal twist and double bars

We present a near-IR, mainly H band, photometry of 72 nearby disk galaxies. The main goal of the survey was to search for isophotal twist inside their nuclear regions. As the twist can be due in some cases to projection effects, rather than resulting from a dynamical phenomenon, we deproject - under the simplifying assumption of a 2D geometry - all galaxies whose disk position angle and inclination are known, the latter not exceeding 75 degrees. We show the ellipticity, position angle and surface brightness radial profiles, and discuss how a projection of 2D and 3D bars can distort the isophotes, give an illusion of a non-existing double bar or mask a real one. We report 15 new double-barred galaxies and confirm 2 detected previously. We identify 14 additional twists not known before and we also find nuclear triaxial structures in three SA galaxies. The frequency of Seyferts among galaxies with nuclear bars or twists is high. As a secondary product, we publish structural parameters (length and axis ratio) of large-scale bars in order to extend still scarce data on bars in the near-IR.Comment: 11 pages of text (Astron. & Astroph. LaTeX l-aa macro) with 3 postscript figures, 7 additional pages of non-main-body postscript figures containing contour and ellipse fitting plots of 72 galaxies; accepted by Astronomy & Astrophysics Suppl. Se

Flat-Cored Dark Matter in Cuspy Clusters of Galaxies

Sand, Treu, & Ellis (2002) have measured the central density profile of cluster MS2137-23 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter distribution within r<50 kpc was fitted by a density cusp of r^{-beta} with beta=0.35. This stands in an apparent contradiction to the CDM prediction of beta~1, and the disagreement worsens if adiabatic compression of the dark matter by the infalling baryons is considered. Following El-Zant, Shlosman & Hoffman (2001), we argue that dynamical friction acting on galaxies moving within the dark matter background counters the effect of adiabatic compression by transfering the orbital energy of galaxies to the dark matter, thus heating up and softening the central density cusp. Using N-body simulations of massive solid clumps moving in clusters we show that indeed the inner dark matter distribution flattens (with beta approx 0.35 for a cluster like MS2137-23) when the galaxies spiral inward. We find as a robust result that while the dark matter distribution becomes core-like, the overall mass distribution preserves its cuspy nature, in agreement with X-ray and lensing observations of clusters.Comment: 7 pages, 3 figures, to be published in Astrophysical Journal Letter