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

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

PCR for the detection of pathogens in neonatal early onset sepsis.

BACKGROUND: A large proportion of neonates are treated for presumed bacterial sepsis with broad spectrum antibiotics even though their blood cultures subsequently show no growth. This study aimed to investigate PCR-based methods to identify pathogens not detected by conventional culture. METHODS: Whole blood samples of 208 neonates with suspected early onset sepsis were tested using a panel of multiplexed bacterial PCRs targeting Streptococcus pneumoniae, Streptococcus agalactiae (GBS), Staphylococcus aureus, Streptococcus pyogenes (GAS), Enterobacteriaceae, Enterococcus faecalis, Enterococcus faecium, Ureaplasma parvum, Ureaplasma urealyticum, Mycoplasma hominis and Mycoplasma genitalium, a 16S rRNA gene broad-range PCR and a multiplexed PCR for Candida spp. RESULTS: Two-hundred and eight samples were processed. In five of those samples, organisms were detected by conventional culture; all of those were also identified by PCR. PCR detected bacteria in 91 (45%) of the 203 samples that did not show bacterial growth in culture. S. aureus, Enterobacteriaceae and S. pneumoniae were the most frequently detected pathogens. A higher bacterial load detected by PCR was correlated positively with the number of clinical signs at presentation. CONCLUSION: Real-time PCR has the potential to be a valuable additional tool for the diagnosis of neonatal sepsis

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ 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 $CP_2$ 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 $CP_2$, 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

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres

Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces

We use a concise method to construct pseudo-automorphisms f_n of the first dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all n > 1 and more generally on the blowups of products of projective spaces. These f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on rational varieties of higher dimensions.Comment: Mathematische Annalen (to appear

Clay Sediments from Basaltic Terrains: Implications for Sedimentary Processes on Mars

The Mars Science Laboratory (MSL) rover, Curiosity, has been traversing across fluvial, lacustrine, and eolian sedimentary rocks since it touched down in 2012. The CheMin X-ray diffractometer (XRD) on board Curiosity has revealed smectite clay minerals in most fluvio-lacustrine samples and abundant X-ray amorphous materials in all samples analyzed to date. For example, mudstones from the Sheepbed member at the base of the stratigraphic section and the lower part of the Murray formation contain on average ~7 to 20 wt% smectite and ~30 to 46 wt% X-ray amorphous abundances. On Earth, smectite and secondary X-ray amorphous materials are juvenile weathering products that are generated in sedimentary environments and ultimately record the interaction between primary igneous minerals and the hydrosphere, atmosphere, and biosphere. For this study, we investigated glacio-fluvio-eolian sediments generated in basaltic terrains as terrestrial analogs for the mudstones from Gale Crater, Mars. This work focuses on the clay sized sediments (<2 m) from these deposits as this grain size hosts the most mineralogically and geochemically altered detritus in sedimentary environments. The goal of investigating basaltic sedimentation is to create a terrestrial reference frame that sheds light on the paleoclimate and paleoaqueous conditions responsible for shaping the ancient sedimentary environments of Mars (e.g., Gale Crater and Jezero Crater)