1,588 research outputs found
Minimality of p-adic rational maps with good reduction
A rational map with good reduction in the field of -adic
numbers defines a -Lipschitz dynamical system on the projective line
over . The dynamical structure of
such a system is completely described by a minimal decomposition. That is to
say, is decomposed into three parts: finitely
many periodic orbits; finite or countably many minimal subsystems each
consisting of a finite union of balls; and the attracting basins of periodic
orbits and minimal subsystems. For any prime , a criterion of minimality for
rational maps with good reduction is obtained. When , a condition in terms
of the coefficients of the rational map is proved to be necessary for the map
being minimal and having good reduction, and sufficient for the map being
minimal and -Lipschitz. It is also proved that a rational map having good
reduction of degree , and can never be minimal on the whole space
.Comment: 21 page
On the fast Khintchine spectrum in continued fractions
For , let be its continued fraction
expansion with partial quotients . Let be a function with as . In this note, the fast Khintchine spectrum, i.e., the Hausdorff
dimension of the set E(\psi):=\Big{x\in [0,1):
\lim_{n\to\infty}\frac{1}{\psi(n)}\sum_{j=1}^n\log a_j(x)=1\Big} is
completely determined without any extra condition on .Comment: 10 page
Research of the active reflector antenna using laser angle metrology system
Active reflector is one of the key technologies for constructing large
telescopes, especially for the millimeter/sub-millimeter radio telescopes. This
article introduces a new efficient laser angle metrology system for the active
reflector antenna of the large radio telescopes, with a plenty of active
reflector experiments mainly about the detecting precisions and the maintaining
of the surface shape in real time, on the 65-meter radio telescope prototype
constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT).
The test results indicate that the accuracy of the surface shape segmenting and
maintaining is up to micron dimension, and the time-response can be of the
order of minutes. Therefore, it is proved to be workable for the sub-millimeter
radio telescopes.Comment: 10 pages, 15 figure
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