3,265 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
Eigenfunctions of the Laplacian and associated Ruelle operator
Let be a co-compact Fuchsian group of isometries on the Poincar\'e
disk \DD and the corresponding hyperbolic Laplace operator. Any
smooth eigenfunction of , equivariant by with real
eigenvalue , where , admits an integral
representation by a distribution \dd_{f,s} (the Helgason distribution) which
is equivariant by and supported at infinity \partial\DD=\SS^1. The
geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension
over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the
so-called Bowen-Series transformation. Let be the complex Ruelle
transfer operator associated to the jacobian . M. Pollicott showed
that \dd_{f,s} is an eigenfunction of the dual operator for the
eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic
eigenfunction of for the eigenvalue 1, given by an
integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}}
\dd_{f,s} (d\eta), \noindent where is a -valued
piecewise constant function whose definition depends upon the geometry of the
Dirichlet fundamental domain representing the surface \DD/\Gamma
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
Color television study Final report, Nov. 1965 - Mar. 1966
Color television camera for transmission from lunar and earth orbits and lunar surfac
Observations on the distribution of Salmonella on primary pig breeding farms
Salmonella infection in pigs has emerged as an important potential public health issue in recent years and several countries have introduced monitoring and control programmes. However, the Salmonella status of most primary breeding herds remains unknown. This paper describes the results of intensive sampling carried out on four occupied primary pig breeding farms and one breeding farm which was purchased and cleaned and disinfected before being used for primary breeding. All premises were sampled intensively by taking large gauze swab samples from every pen of breeding sows, boars and rearing gilt and boar progeny. Samples of equipment and faeces plus carcases of wildlife vectors were also collected. On one farm (A) S. Derby, S. Kedougou and S. Newport were found in all locations whereas S. Typhimurium (DT1 04, DT20) was restricted to gilts retained for the herd and gilts and boars being reared for sale. There was considerable involvement of rodents and evidence of ineffective disinfection of farrowing crates. On a second farm (B), owned by the same company, there were similar findings, with S. Meleagridis also present. Improvements to rodent control but not disinfection produced no reduction in the overall prevalence of Salmonella. On two other farms, belonging to a separate company, S. Give predominated in adult breeding stock and rearing gilts and boars but some S. Typhimurium (OT1 04, DT193) was also present in the young stock on the larger unit (C). In the smaller unit (D), in which hygiene and rodent control was much better, only S. Give and S. Kedougou were found. In another farm (E) S. Stanley, S. Bredeney, S. Mbandaka and S. Typhimurium were found before total depopulation. Cleaning and disinfection was poor initially but successful after improvements, but no sampling was permitted in the new primary breeding herd by the new owners of the arm
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
Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
First we prove a new inequality comparing uniformly the relative volume of a
Borel subset with respect to any given complex euclidean ball \B \sub \C^n
with its relative logarithmic capacity in \C^n with respect to the same ball
\B.
An analoguous comparison inequality for Borel subsets of euclidean balls of
any generic real subspace of \C^n is also proved.
Then we give several interesting applications of these inequalities.
First we obtain sharp uniform estimates on the relative size of \psh
lemniscates associated to the Lelong class of \psh functions of logarithmic
singularities at infinity on \C^n as well as the Cegrell class of
\psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W
\Sub \C^n.
Then we also deduce new results on the global behaviour of both the Lelong
class and the Cegrell class of \psh functions.Comment: 25 page
Canalization of the evolutionary trajectory of the human influenza virus
Since its emergence in 1968, influenza A (H3N2) has evolved extensively in
genotype and antigenic phenotype. Antigenic evolution occurs in the context of
a two-dimensional 'antigenic map', while genetic evolution shows a
characteristic ladder-like genealogical tree. Here, we use a large-scale
individual-based model to show that evolution in a Euclidean antigenic space
provides a remarkable correspondence between model behavior and the
epidemiological, antigenic, genealogical and geographic patterns observed in
influenza virus. We find that evolution away from existing human immunity
results in rapid population turnover in the influenza virus and that this
population turnover occurs primarily along a single antigenic axis. Thus,
selective dynamics induce a canalized evolutionary trajectory, in which the
evolutionary fate of the influenza population is surprisingly repeatable and
hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure
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