2,735 research outputs found
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic
diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps
has been studied by a number of authors. We refer to [BLS] for a general
introduction to this class of dynamical systems. An interesting object from the
point of view of potential theory is the equilibrium measure of the set
of points with bounded orbits. In [BLS] is also characterized
dynamically as the unique measure of maximal entropy. Thus is also an
equilibrium measure from the point of view of the thermodynamical formalism. In
the present paper we give another dynamical interpretation of as the
limit distribution of the periodic points of
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
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
Practice pointer: Using the new UK-WHO growth charts
The new UK growth charts for children aged 0-4 years (designed using data from the new WHO standards) describe the optimal pattern of growth for all children, rather than the prevailing pattern in the UK (as with previous charts).
The new charts are suitable for all ethnic groups and set breast feeding as the norm.
UK children match the new charts well for length and height, but after age 6 months fewer children will be below the 2nd centile for weight or show weight faltering, and more will be above the 98th centile.
The new charts look different: they have a separate preterm section, no lines between 0 and 2 weeks, and the 50th percentile is no longer emphasised.
The charts give clear instructions on gestational correction, and there is a new chart for infants born before 32 weeks’ gestation.
The instructions advise on when and how to measure and when a measurement or growth pattern is outside the normal range.
The charts include a “look-up” tool for determining the body mass index centile from height and weight centiles without calculation and aid for predicting adult height.
The charts and supporting educational materials can be downloaded from www.growthcharts.rcpch.ac.u
Decorrelation Stretches (DCS) of Visible Images as a Tool for Sedimentary Provenance Investigations on Earth and Mars
The surface of Mars exhibits vast expanses of mafic sediments and ancient sedimentary rocks that record signals of climate and environment. To decipher the paleoenvironments, the sediment sources and transport histories must be con-strained, but it is not well known how physical fractionation and aqueous alteration affect mafic sediments during glacial, eolian, and fluvial processes. Semi-Autonomous Navigation for Detrital Environments (SAND-E), a NASA Planetary Science and Technology through Analog Research (PSTAR) project, bridges this gap through studies of sediment-grain properties and mineralogy in the glacio-XRD)-derived mineralogies
Families of strictly pseudoconvex domains and peak functions
We prove that given a family of strictly pseudoconvex domains varying
in topology on domains, there exists a continuously varying
family of peak functions for all at every $\zeta\in\partial
G_t.
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
Sediment Sorting and Rounding in a Basaltic Glacio-Fluvio-Aeolian Environment: hrisjkull Glacier, Iceland
Sediments and sedimentary rocks preserve a rich history of environment and climate. Identifying these signals requires an understanding of the physical and chemical processes that have affected sedimentary deposits [1]. Such processes include sorting and rounding during transport and chemical alteration through weathering and diagenesis. Although these processes have long been studied in quartz-dominated sedimentary systems [2], a lack of studies of basaltic sedimentary systems limits our interpretations of the environment and climate where mafic source rocks dominate, such as on Mars [3,4]. As part of the SAND-E: Semi-Autonomous Navigation for Detrital Environments project [5], which uses robotic operations to examine physical and chemical changes to sediments in basaltic glacio-fluvialaeolian environments, this research studies changes in sorting and rounding of fluvial-aeolian sediments along a glacier-proximal-to-glacier-distal transect in the outwash-plain of the risjkull glacier in SW Iceland (Fig. 1
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