4,553 research outputs found
Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces
In this paper we show that totally geodesic subspaces determine the
commensurability class of a standard arithmetic hyperbolic -orbifold, . Many of the results are more general and apply to locally symmetric spaces
associated to arithmetic lattices in -simple Lie groups of type
and . We use a combination of techniques from algebraic groups and
quadratic forms to prove several results about these spaces.Comment: 34 Pages. Corrected typos. Added references. Improved expositio
Periodicity and Growth in a Lattice Gas with Dynamical Geometry
We study a one-dimensional lattice gas "dynamical geometry model" in which
local reversible interactions of counter-rotating groups of particles on a ring
can create or destroy lattice sites. We exhibit many periodic orbits and and
show that all other solutions have asymptotically growing lattice length in
both directions of time. We explain why the length grows as in all
cases examined. We completely solve the dynamics for small numbers of particles
with arbitrary initial conditions.Comment: 18 pages, LaTe
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