402,168 research outputs found
Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang
We prove that a real analytic subset of a torus group that is contained in
its image under an expanding endomorphism is a finite union of translates of
closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and
Wang for real analytic varieties. Our proof uses real analytic geometry,
topological dynamics and Fourier analysis.Comment: 25 page
GLAMER Part II: Multiple Plane Gravitational Lensing
We present an extension to multiple planes of the gravitational lensing code
{\small GLAMER}. The method entails projecting the mass in the observed
light-cone onto a discrete number of lens planes and inverse ray-shooting from
the image to the source plane. The mass on each plane can be represented as
halos, simulation particles, a projected mass map extracted form a numerical
simulation or any combination of these. The image finding is done in a source
oriented fashion, where only regions of interest are iteratively refined on an
initially coarse image plane grid. The calculations are performed in parallel
on shared memory machines. The code is able to handle different types of
analytic halos (NFW, NSIE, power-law, etc.), haloes extracted from numerical
simulations and clusters constructed from semi-analytic models ({\small MOKA}).
Likewise, there are several different options for modeling the source(s) which
can be distributed throughout the light-cone. The distribution of matter in the
light-cone can be either taken from a pre-existing N-body numerical
simulations, from halo catalogs, or are generated from an analytic mass
function. We present several tests of the code and demonstrate some of its
applications such as generating mock images of galaxy and galaxy cluster
lenses.Comment: 14 pages, 10 figures, submitted to MNRA
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