9,287 research outputs found
Hyperbolic Components in Exponential Parameter Space
We discuss the space of complex exponential maps \Ek\colon z\mapsto
e^{z}+\kappa. We prove that every hyperbolic component has connected
boundary, and there is a conformal isomorphism \Phi_W\colon W\to\half^- which
extends to a homeomorphism of pairs \Phi_W\colon(\ovl
W,W)\to(\ovl\half^-,\half^-). This solves a conjecture of Baker and Rippon,
and of Eremenko and Lyubich, in the affirmative. We also prove a second
conjecture of Eremenko and Lyubich.Comment: To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description
of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figur
Rational parameter rays of the Mandelbrot set
We give a new proof that all external rays of the Mandelbrot set at rational
angles land, and of the relation between the external angle of such a ray and
the dynamics at the landing point. Our proof is different from the original
one, given by Douady and Hubbard and refined by Lavaurs, in several ways: it
replaces analytic arguments by combinatorial ones; it does not use complex
analytic dependence of the polynomials with respect to parameters and can thus
be made to apply for non-complex analytic parameter spaces; this proof is also
technically simpler. Finally, we derive several corollaries about hyperbolic
components of the Mandelbrot set. Along the way, we introduce partitions of
dynamical and parameter planes which are of independent interest, and we
interpret the Mandelbrot set as a symbolic parameter space of kneading
sequences and internal addresses.Comment: 33 pages, 9 figure
The Highly Unusual Outgassing of Comet 103P/Hartley 2 from Narrowband Photometry and Imaging of the Coma
We report on photometry and imaging of Comet 103P/Hartley 2 obtained at
Lowell Observatory from 1991 through 2011. We acquired photoelectric photometry
on two nights in 1991, four nights in 1997/98, and 13 nights in 2010/11. We
observed a strong secular decrease in water and all other observed species
production in 2010/11 from the 1991 and 1997/98 levels. We see evidence for a
strong asymmetry with respect to perihelion in the production rates of our
usual bandpasses, with peak production occurring ~10 days post-perihelion and
production rates considerably higher post-perihelion. The composition was
"typical", in agreement with the findings of other investigators. We obtained
imaging on 39 nights from 2010 July until 2011 January. We find that, after
accounting for their varying parentage and lifetimes, the C2 and C3 coma
morphology resemble the CN morphology we reported previously. These species
exhibited an hourglass shape in October and November, and the morphology
changed with rotation and evolved over time. The OH and NH coma morphology
showed hints of an hourglass shape near the nucleus, but was also enhanced in
the anti-sunward hemisphere. This tailward brightness enhancement did not vary
significantly with rotation and evolved with the viewing geometry. We conclude
that all five gas species likely originate from the same source regions on the
nucleus, but that OH and NH were derived from small grains of water and ammonia
ice that survived long enough to be affected by radiation pressure and driven
in the anti-sunward direction. We detected the faint, sunward facing dust jet
reported by other authors, and did not detect a corresponding gas feature. This
jet varied little during a night but exhibited some variations from night to
night, suggesting it is located near the total angular momentum vector.Comment: Accepted by Icarus; 20 pages of text (preprint style), 5 tables, 7
figure
Geologic transcript from Apollo 11 mission
Quick time transcript of lunar geology from Apollo 1
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