Integrability of dominated decompositions on three-dimensional manifolds

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions

Integrability of continuous bundles

We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we derive new criteria for uniqueness of solutions to ODE's and PDE's and for the integrability of invariant bundles in dynamical systems. In particular we give a novel proof of the Stable Manifold Theorem and prove some integrability results for dynamically defined dominated splittings

Decay of correlations in one-dimensional dynamics

We consider multimodal C3 interval maps f satisfying a summability condition on the derivatives Dn along the critical orbits which implies the existence of an absolutely continuous f-invariant probability measure mu. If f is non-renormalizable, mu is mixing and we show that the speed of mixing (decay of correlations) is strongly related to the rate of growth of the sequence (Dn) as n → infinity. We also give sufficient conditions for mu to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations.</p

Statistical stability and limit laws for Rovella maps

We consider the family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that there is a one-parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrent to the critical point. Metzger proved that these maps have a unique absolutely continuous ergodic invariant probability measure (SRB measure). Here we use the technique developed by Freitas and show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the continuous variation of the densities of the SRB measures and associated metric entropies with the parameter. Our main result also implies some statistical properties for these maps.Comment: 1 figur

Some remarks on the geometry of the Standard Map

We define and compute hyperbolic coordinates and associated foliations which provide a new way to describe the geometry of the standard map. We also identify a uniformly hyperbolic region and a complementary 'critical' region containing a smooth curve of tangencies between certain canonical 'stable' foliations.Comment: 25 pages, 11 figure

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Urban society and the English Revolution : the archaeology of the new Jerusalem

The English Revolution has long been a defining subject of English historiography, with a large and varied literature that reflects continuing engagement with the central themes of civil conflict, and deep-rooted social, political and religious change. By contrast, this period has failed to catch the imagination of archaeologists. This research seeks to understand the world of the English Revolution through its material expression in English towns. Identifying the material expressions of the period is central to developing an archaeological understanding of the period. The clearest material expressions are found, in the fortifications that were built to protect towns, the destruction that was wrought on towns and in the reconstruction of the material world of English towns. Towns, like any other artefact, have their meanings. These meanings are multivalent and ever shifting, defined by the interaction of their material fabric and those who experience it. As these meanings change over time, they can be traced through the structures and artefacts of the town, and through the myths and legends that accrete on them. Understanding the interactions of material, myth and memory allows archaeologists to understand the true meaning of the urban built environment to generate a deeper and more nuanced understanding of the nature of the English urban culture of the period. Towns were fundamental to the English imagination as much as they were economically, politically or socially important. The English Revolution sits at the heart of the accepted conception of historical archaeology, but has been curiously neglected by historical archaeologists. The cultural conflict of this period embodies the themes that are central to historical archaeology, and nowhere is this more apparent than in urban culture.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Patients with paroxysmal nocturnal hemoglobinuria have a high frequency of peripheral-blood T cells expressing activating isoforms of inhibiting superfamily receptors

Patients with paroxysmal nocturnal hemoglobinuria (PNH) have a large clonal population of blood cells deriving from hematopoietic stem cells (HSCs) deficient in glycosylphosphatidylinositol (GPI)-anchored surface molecules. A current model postulates that PNH arises through negative selection against normal HSCs exerted by autoreactive T cells, whereas PNH HSCs escape damage. We have investigated the inhibitory receptor superfamily (IRS) system in 13 patients with PNH. We found a slight increase in the proportion of T cells expressing IRS. In contrast to what applies to healthy donors, the engagement of IRS molecules on T cells from patients with PNH elicited a powerful cytolytic activity in a redirected killing assay, indicating that these IRSs belong to the activating type. This was confirmed by clonal analysis: 50% of IRS+ T-cell clones in patients with PNH were of the activating type, while only 5% were of the activating type in healthy donors. Moreover, the ligation of IRS induces (1) production of tumor necrosis factor alpha (TNF-alpha) and interferon gamma (IFN-gamma) and (2) brisk cytolytic activity against cells bearing appropriate IRS counter-ligands. In addition, these IRS+ T cells show natural killer (NK)-like cytolytic activity to which GPI- cells were less sensitive than GPI+ cells. Thus, T cells with NK-like features, expressing the activating isoforms of IRS, may include effector cells involved in the pathogenesis of PNH