53 research outputs found
EP-1097: Comparison of outcomes and toxicities between IMRT and SIB-IMRT in cancers of hypopharynx
Monodromy of Cyclic Coverings of the Projective Line
We show that the image of the pure braid group under the monodromy action on
the homology of a cyclic covering of degree d of the projective line is an
arithmetic group provided the number of branch points is sufficiently large
compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae
Arithmeticity vs. non-linearity for irreducible lattices
We establish an arithmeticity vs. non-linearity alternative for irreducible
lattices in suitable product groups, such as for instance products of
topologically simple groups. This applies notably to a (large class of)
Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as
we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page
The Asymptotic distribution of circles in the orbits of Kleinian groups
Let P be a locally finite circle packing in the plane invariant under a
non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When
Gamma is geometrically finite, we construct an explicit Borel measure on the
plane which describes the asymptotic distribution of small circles in P,
assuming that either the critical exponent of Gamma is strictly bigger than 1
or P does not contain an infinite bouquet of tangent circles glued at a
parabolic fixed point of Gamma. Our construction also works for P invariant
under a geometrically infinite group Gamma, provided Gamma admits a finite
Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite.
Some concrete circle packings to which our result applies include Apollonian
circle packings, Sierpinski curves,
Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat
Lyapunov exponents for products of complex Gaussian random matrices
The exact value of the Lyapunov exponents for the random matrix product with each , where
is a fixed positive definite matrix and a complex Gaussian matrix with entries standard complex normals, are
calculated. Also obtained is an exact expression for the sum of the Lyapunov
exponents in both the complex and real cases, and the Lyapunov exponents for
diffusing complex matrices.Comment: 15 page
Multidimensional continued fractions, dynamical renormalization and KAM theory
The disadvantage of `traditional' multidimensional continued fraction
algorithms is that it is not known whether they provide simultaneous rational
approximations for generic vectors. Following ideas of Dani, Lagarias and
Kleinbock-Margulis we describe a simple algorithm based on the dynamics of
flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of
covolume one) that indeed yields best possible approximations to any irrational
vector. The algorithm is ideally suited for a number of dynamical applications
that involve small divisor problems. We explicitely construct renormalization
schemes for (a) the linearization of vector fields on tori of arbitrary
dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page
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