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Discrete Subgroups of Semisimple Lie Groups
1. Statement of Main Results.- 2. Synopsis of the Chapters.- 3. Remarks on the Structure of the Book, References and Notation.- 1. Preliminaries.- 0. Notation, Terminology and Some Basic Facts.- 1.
Flows on homogeneous spaces and Diophantine approximation on manifolds
We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous
Logarithm laws for flows on homogeneous spaces
Abstract.In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of subsets {At | t∈ℕ} of a homogeneous space G/Γ (G a semisimple Lie
Explicit constructions of graphs without short cycles and low density codes
We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to
Semigroups containing proximal linear maps
A linear automorphism of a finite dimensional real vector spaceV is calledproximal if it has a unique eigenvalue—counting multiplicities—of maximal modulus. Goldsheid and Margulis have shown that if
Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
Notation. The main objects of this paper are n-tuples y = (y1, . . . , yn) of real numbers viewed as linear forms, i.e. as row vectors. In what follows, y will always mean a row vector, and we will
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