17,809 research outputs found
Stable dynamics in forced systems with sufficiently high/low forcing frequency
We consider a class of parametrically forced Hamiltonian systems with
one-and-a-half degrees of freedom and study the stability of the dynamics when
the frequency of the forcing is relatively high or low. We show that, provided
the frequency of the forcing is sufficiently high, KAM theorem may be applied
even when the forcing amplitude is far away from the perturbation regime. A
similar result is obtained for sufficiently low frequency forcing, but in that
case we need the amplitude of the forcing to be not too large; however we are
still able to consider amplitudes of the forcing which are outside of the
perturbation regime. Our results are illustrated by means of numerical
simulations for the system of a forced cubic oscillator. In addition, we find
numerically that the dynamics are stable even when the forcing amplitude is
very large (beyond the range of validity of the analytical results), provided
the frequency of the forcing is taken correspondingly low.Comment: 12 pages, 3 figures, 2 table
Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition
Let be a set of pairwise disjoint unit disks in the plane.
We describe how to build a data structure for so that for any
point set containing exactly one point from each disk, we can quickly find
the onion decomposition (convex layers) of .
Our data structure can be built in time and has linear size.
Given , we can find its onion decomposition in time, where
is the number of layers. We also provide a matching lower bound. Our solution
is based on a recursive space decomposition, combined with a fast algorithm to
compute the union of two disjoint onionComment: 10 pages, 5 figures; a preliminary version appeared at WADS 201
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