2,654 research outputs found
Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
This paper concerns the dynamics of polynomial automorphisms of .
One can associate to such an automorphism two currents and the
equilibrium measure . In this paper we study some
geometric and dynamical properties of these objects. First, we characterize
as the unique measure of maximal entropy. Then we show that the measure
has a local product structure and that the currents have a
laminar structure. This allows us to deduce information about periodic points
and heteroclinic intersections. For example, we prove that the support of
coincides with the closure of the set of saddle points. The methods used
combine the pluripotential theory with the theory of non-uniformly hyperbolic
dynamical systems
The Dual Feminisation of HIV/AIDS
This is an Accepted Manuscript of an article published by Taylor & Francis in Globalizations on 2011, available online: http://wwww.tandfonline.com/10.1080/14747731.2010.49302
Adding flavour to twistor strings
Twistor string theory is known to describe a wide variety of field theories
at tree-level and has proved extremely useful in making substantial progress in
perturbative gauge theory. We explore the twistor dual description of a class
of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding
'flavour' branes to the topological B-model on super-twistor space and comment
on the appearance of these objects. Evidence for the correspondence is provided
by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical
Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3:
Typos correcte
Nowhere minimal CR submanifolds and Levi-flat hypersurfaces
A local uniqueness property of holomorphic functions on real-analytic nowhere
minimal CR submanifolds of higher codimension is investigated. A sufficient
condition called almost minimality is given and studied. A weaker necessary
condition, being contained a possibly singular real-analytic Levi-flat
hypersurface is studied and characterized. This question is completely resolved
for algebraic submanifolds of codimension 2 and a sufficient condition for
noncontainment is given for non algebraic submanifolds. As a consequence, an
example of a submanifold of codimension 2, not biholomorphically equivalent to
an algebraic one, is given. We also investigate the structure of singularities
of Levi-flat hypersurfaces.Comment: 21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom.
Ana
Letter from John Waddell, et al. to George Sibley, July 17, 1834
Transcript of Letter from John Waddell, et al. to George Sibley, July 17, 1834. Waddell and others discuss hard and liberal Whigs; Missouri politics
Post-critical set and non existence of preserved meromorphic two-forms
We present a family of birational transformations in depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in is first carried out
using Diller-Favre criterion in order to find the complexity reduction of the
mapping. The integrable cases are found. The identification between the
complexity growth and the topological entropy is, one more time, verified. We
perform plots of the post-critical set, as well as calculations of Lyapunov
exponents for many orbits, confirming that generically no meromorphic two-form
can be preserved for this mapping. These birational transformations in ,
which, generically, do not preserve any meromorphic two-form, are extremely
similar to other birational transformations we previously studied, which do
preserve meromorphic two-forms. We note that these two sets of birational
transformations exhibit totally similar results as far as topological
complexity is concerned, but drastically different results as far as a more
``probabilistic'' approach of dynamical systems is concerned (Lyapunov
exponents). With these examples we see that the existence of a preserved
meromorphic two-form explains most of the (numerical) discrepancy between the
topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure
Characterisation of Float Rocks at Ireson Hill, Gale Crater
Float rocks discovered by surface missions on Mars have given unique insights into the sedimentary, diagenetic and igneous processes that have operated throughout the planets history. In addition, Gale sedimentary rocks, both float and in situ, record a combination of source compositions and diagenetic overprints. We examine a group of float rocks that were identified by the Mars Science Laboratory missions Curiosity rover at the Ireson Hill site, circa. sol 1600 using ChemCam LIBS, APXS and images from the MastCam, Mars Hand Lens Imager (MAHLI) and ChemCam Remote Micro-Imager (RMI) cameras. Geochemical data provided by the APXS and ChemCam instruments allow us to compare the compositions of these rocks to known rock types from Gale crater, as well as elsewhere on Mars. Ireson Hill is a 15 m long butte in the Murray formation with a dark cap-ping unit with chemical and stratigraphic consistency with the Stimson formation. A total of 6 float rocks have been studied on the butte
Problems and Aspects of Energy-Driven Wavefunction Collapse Models
Four problematic circumstances are considered, involving models which
describe dynamical wavefunction collapse toward energy eigenstates, for which
it is shown that wavefunction collapse of macroscopic objects does not work
properly. In one case, a common particle position measuring situation, the
apparatus evolves to a superposition of macroscopically distinguishable states
(does not collapse to one of them as it should) because each such
particle/apparatus/environment state has precisely the same energy spectrum.
Second, assuming an experiment takes place involving collapse to one of two
possible outcomes which is permanently recorded, it is shown in general that
this can only happen in the unlikely case that the two apparatus states
corresponding to the two outcomes have disjoint energy spectra. Next, the
progressive narrowing of the energy spectrum due to the collapse mechanism is
considered. This has the effect of broadening the time evolution of objects as
the universe evolves. Two examples, one involving a precessing spin, the other
involving creation of an excited state followed by its decay, are presented in
the form of paradoxes. In both examples, the microscopic behavior predicted by
standard quantum theory is significantly altered under energy-driven collapse,
but this alteration is not observed by an apparatus when it is included in the
quantum description. The resolution involves recognition that the statevector
describing the apparatus does not collapse, but evolves to a superposition of
macroscopically different states.Comment: 17 page
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