3,229 research outputs found
Dynamics of horizontal-like maps in higher dimension
We study the regularity of the Green currents and of the equilibrium measure
associated to a horizontal-like map in C^k, under a natural assumption on the
dynamical degrees. We estimate the speed of convergence towards the Green
currents, the decay of correlations for the equilibrium measure and the
Lyapounov exponents. We show in particular that the equilibrium measure is
hyperbolic. We also show that the Green currents are the unique invariant
vertical and horizontal positive closed currents. The results apply, in
particular, to Henon-like maps, to regular polynomial automorphisms of C^k and
to their small pertubations.Comment: Dedicated to Professor Gennadi Henkin on the occasion of his 65th
birthday, 37 pages, to appear in Advances in Mat
A theorem of Tits type for compact Kahler manifolds
We prove a theorem of Tits type about automorphism groups for compact Kahler
manifolds, which has been conjectured in the paper [KOZ].Comment: Inventiones Mathematicae (to appear), 11 page
Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces
We use a concise method to construct pseudo-automorphisms f_n of the first
dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all
n > 1 and more generally on the blowups of products of projective spaces. These
f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first
examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on
rational varieties of higher dimensions.Comment: Mathematische Annalen (to appear
Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds
We consider the dynamics of meromorphic maps of compact K\"ahler manifolds.
In this work, our goal is to locate the non-nef locus of invariant classes and
provide necessary and sufficient conditions for existence of Green currents in
codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and
Theorem 5.3 are adde
Sur les exposants de Lyapounov des applications meromorphes
Let f be a dominating meromorphic self-map of a compact Kahler manifold. We
give an inequality for the Lyapounov exponents of some ergodic measures of f
using the metric entropy and the dynamical degrees of f. We deduce the
hyperbolicity of some measures.Comment: 27 pages, paper in french, final version: to appear in Inventiones
Mat
Parametric attosecond pulse amplification far from the ionization threshold from high order harmonic generation in He
Parametric amplification of attosecond coherent pulses around 100 eV at the
single-atom level is demonstrated for the first time by using the 3D
time-dependent Schr{\"o}dinger equation in high-harmonic generation processes
from excited states of He. We present the attosecond dynamics of the
amplification process far from the ionization threshold and resolve the physics
behind it. The amplification of a particular central photon energy requires the
seed XUV pulses to be perfectly synchronized in time with the driving laser
field for stimulated recombination to the He ground state and is only
produced in a few specific laser cycles in agreement with the experimental
measurements. Our simulations show that the amplified photon energy region can
be controlled by varying the peak intensity of the laser field. Our results
pave the way to the realization of compact attosecond pulse intense XUV lasers
with broad applications
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