5,593 research outputs found
Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system
The Mishchenko-Fomenko theorem on superintegrable Hamiltonian systems is
generalized to superintegrable Hamiltonian systems with noncompact invariant
submanifolds. It is formulated in the case of globally superintegrable
Hamiltonian systems which admit global generalized action-angle coordinates.
The well known Kepler system falls into two different globally superintegrable
systems with compact and noncompact invariant submanifolds.Comment: 23 page
The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810
The concept of a symplectic structure first appeared in the works of Lagrange
on the so-called "method of variation of the constants". These works are
presented, together with those of Poisson, who first defined the composition
law called today the "Poisson bracket". The method of variation of the
constants is presented using today's mathematical concepts and notations.Comment: Presented at the meeting "Poisson 2008" in Lausanne, July 2008.
Published in Letters in Mathematical Physics. 22 page
Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras
We describe the group of continuous automorphisms of all simple
infinite-dimensional linearly compact Lie superalgebras and use it in order to
classify F-forms of these superalgebras over any field F of characteristic
zero.Comment: 24 page
Cohomology of GKM Fiber Bundles
The equivariant cohomology ring of a GKM manifold is isomorphic to the
cohomology ring of its GKM graph. In this paper we explore the implications of
this fact for equivariant fiber bundles for which the total space and the base
space are both GKM and derive a graph theoretical version of the Leray-Hirsch
theorem. Then we apply this result to the equivariant cohomology theory of flag
varieties.Comment: The paper has been accepted by the Journal of Algebraic
Combinatorics. The final publication is available at springerlink.co
Mg II Absorption Systems in SDSS QSO Spectra
We present the results of a MgII absorption-line survey using QSO spectra
from the SDSS EDR. Over 1,300 doublets with rest equivalent widths greater than
0.3\AA and redshifts were identified and measured. We
find that the rest equivalent width ()
distribution is described very well by an exponential function , with
and \AA. Previously reported power law
fits drastically over-predict the number of strong lines. Extrapolating our
exponential fit under-predicts the number of \AA systems,
indicating a transition in near \AA. A combination of
two exponentials reproduces the observed distribution well, suggesting that
MgII absorbers are the superposition of at least two physically distinct
populations of absorbing clouds. We also derive a new redshift parameterization
for the number density of \AA lines:
and \AA. We find that the distribution steepens with decreasing redshift,
with decreasing from \AA at to \AA at
. The incidence of moderately strong MgII lines does not
show evidence for evolution with redshift. However, lines stronger than
\AA show a decrease relative to the no-evolution prediction with
decreasing redshift for . The evolution is stronger for
increasingly stronger lines. Since in saturated absorption lines is an
indicator of the velocity spread of the absorbing clouds, we interpret this as
an evolution in the kinematic properties of galaxies from moderate to low z.Comment: 50 pages, 26 figures, accepted for publication in Ap
QSOs and Absorption Line Systems Surrounding the Hubble Deep Field
We have imaged a 45x45 sq. arcmin. area centered on the Hubble Deep Field
(HDF) in UBVRI passbands, down to respective limiting magnitudes of
approximately 21.5, 22.5, 22.2, 22.2, and 21.2. The principal goals of the
survey are to identify QSOs and to map structure traced by luminous galaxies
and QSO absorption line systems in a wide volume containing the HDF. We have
selected QSO candidates from color space, and identified 4 QSOs and 2 narrow
emission-line galaxies (NELGs) which have not previously been discovered,
bringing the total number of known QSOs in the area to 19. The bright z=1.305
QSO only 12 arcmin. away from the HDF raises the northern HDF to nearly the
same status as the HDF-S, which was selected to be proximate to a bright QSO.
About half of the QSO candidates remain for spectroscopic verification.
Absorption line spectroscopy has been obtained for 3 bright QSOs in the field,
using the Keck 10m, ARC 3.5m, and MDM 2.4m telescopes. Five heavy-element
absorption line systems have been identified, 4 of which overlap the
well-explored redshift range covered by deep galaxy redshift surveys towards
the HDF. The two absorbers at z=0.5565 and z=0.5621 occur at the same redshift
as the second most populated redshift peak in the galaxy distribution, but each
is more than 7Mpc/h (comoving, Omega_M=1, Omega_L=0) away from the HDF line of
sight in the transverse dimension. This supports more indirect evidence that
the galaxy redshift peaks are contained within large sheet-like structures
which traverse the HDF, and may be precursors to large-scale ``pancake''
structures seen in the present-day galaxy distribution.Comment: 36 pages, including 9 figures and 8 tables. Accepted for publication
in the Astronomical Journa
Quantum ergodicity of C* dynamical systems
This paper contains a very simple and general proof that eigenfunctions of
quantizations of classically ergodic systems become uniformly distributed in
phase space. This ergodicity property of eigenfunctions f is shown to follow
from a convexity inequality for the invariant states (Af,f). This proof of
ergodicity of eigenfunctions simplifies previous proofs (due to A.I.
Shnirelman, Colin de Verdiere and the author) and extends the result to the
much more general framework of C* dynamical systems.Comment: Only very minor differences with the published versio
Invariants of pseudogroup actions: Homological methods and Finiteness theorem
We study the equivalence problem of submanifolds with respect to a transitive
pseudogroup action. The corresponding differential invariants are determined
via formal theory and lead to the notions of k-variants and k-covariants, even
in the case of non-integrable pseudogroup. Their calculation is based on the
cohomological machinery: We introduce a complex for covariants, define their
cohomology and prove the finiteness theorem. This implies the well-known
Lie-Tresse theorem about differential invariants. We also generalize this
theorem to the case of pseudogroup action on differential equations.Comment: v2: some remarks and references addee
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