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Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
Horocyclic Flows Complete Hyperbolic Surfaces Finite Area
2015/8/26
We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution ...
Skinning measures in negative curvature and equidistribution of equidistant submanifolds
Mixing equidistribution rate of mixing decay of correlation negative curvature
2012/3/1
Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back Patterson-Sullivan's measures at...
Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution
singular perturbation adaptive grid rate of convergence error estimate
2011/10/13
We derive varepsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here,...
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
Equidistribution of Eisenstein series convex co-compact hyperbolic manifolds Spectral Theory
2011/9/5
Abstract: For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisens...
Equidistribution of cusp forms in the level aspect
Equidistribution cusp forms level aspect
2010/11/11
Let f traverse a sequence of classical holomorphic newforms of fixed weight and increasing squarefree level q tending to infinity. We prove that the pushforward of the mass of f to the modular curve o...
Equidistribution speed towards the Green current for endomorphisms of P^k
the Green current endomorphisms of P^k
2010/11/9
Let f be a non-invertible holomorphic endomorphism of P^k. For a hypersurface H of P^k, generic in the Zariski sense, we give an explicit speed of convergence of f^{-n}(H) towards the dynamical Green ...
Mass equidistribution of Hilbert modular eigenforms
Mass equidistribution Hilbert modular eigenforms
2010/11/11
Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show th...
On Arnold's and Kazhdan's equidistribution problems
Arnold's Kazhdan's equidistribution problems
2010/12/13
We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that
the action has a...