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 $\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\mu$ as the limit distribution of the periodic points of $f$

Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ 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

Array E system description

This ATM describes the ALSEP Array E System. Its main purpose is to convey an understanding of the Power and Data Subsystems operation to a depth just above the circuit schematic level.written by A. Bedford, J. Kasser, D. Thomas ; approved by D. Fithian.General -- Structure/thermal subsystem -- Power subsystem -- Data subsystem -- Array "E" scientific instrument

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

Identifying entanglement using quantum "ghost" interference and imaging

We report a quantum interference and imaging experiment which quantitatively demonstrates that Einstein-Podolsky-Rosen (EPR) type entangled two-photon states exhibit both momentum-momentum and position-position correlations, stronger than any classical correlation. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities D(k1+k2)<min(D(k1),D(k2)) and D(x1-x2)<min(D(x1),D(x2)). These two inequalities, together, represent a non-classicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for two-photons/two photons systems.Comment: We have changed Eq.(2) from one inequality to two inequalities. The two expressions are actually consistent with each other, but the new one represents a more stringent condition for entanglement and, in our opinion, better explains the original idea of EPR. We have clarified this point in the paper. 4 pages; submitted to PR

Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ 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 $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ 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 $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma

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

Using XRD to Characterize Sediment Sorting in a Mars Analog Glacio-Fluvio-Eolian Basaltic Sedimentary System in Iceland

The martian surface has a primarily basaltic composition and is dominated by sedimentary deposits. Ancient layered sedimentary rocks have been identified across the planet from orbit, have been studied in situ by the Mars Exploration Rovers and the Mars Science Laboratory rover, and will be studied by the Mars 2020 rover. These ancient sedimentary rocks were deposited in fluvial, lacustrine, and eolian environments during a warmer and wetter era on Mars. It is important to study the composition of sediments in Mars analog environments to characterize how minerals in basaltic sedimentary systems are sorted and/or aqueously altered. This information can help us better interpret sedimentary processes from similar deposits on Mars and derive information about the igneous source rocks. Sediment sorting has been studied extensively on Earth, but not typically in basaltic environments. Previous work has addressed sorting of basaltic sediments through experimental techniques and in modern eolian basaltic systems and aqueous alteration in subglacial and proglacial environments. We add to this body of research by studying sediment sorting and aqueous alteration in a glacio-fluvio-eolian basaltic system in southwest Iceland