37 research outputs found
Invariant graphs of a family of non-uniformly expanding skew products over Markov maps
We consider a family of skew-products of the form where is a continuous expanding Markov
map and is a family of homeomorphisms of
. A function is said to be an invariant graph
if is an invariant set for the
skew-product; equivalently if . A well-studied problem is
to consider the existence, regularity and dimension-theoretic properties of
such functions, usually under strong contraction or expansion conditions (in
terms of Lyapunov exponents or partial hyperbolicity) in the fibre direction.
Here we consider such problems in a setting where the Lyapunov exponent in the
fibre direction is zero on a set of periodic orbits. We prove that either
has the structure of a `quasi-graph' (or `bony graph') or is as smooth as the
dynamics, and we give a criteria for this to happen.Comment: 21 pages, 2 figure
An unusual case of hypertrophic cardiomyopathy causing right ventricular outflow tract obstruction
Loop spaces and choreographies in dynamical systems
We consider a subset of the set of solutions to the n-body problem, termed choreographies, which involve a motion of particles where each follows the same path in space with a fixed time delay. Focusing on planar choreographies, we use the action of symmetry groups on the spatial and temporal motion of such systems to restrict a space of loops and study the topology of the resulting manifolds. As well as providing a framework of notation and terminology for the study of such systems, we prove various useful properties which allow us to classify the possible groups of symmetries, and discuss which are likely to be realisable as that of a motion of bodies.EThOS - Electronic Theses Online ServiceForrest RecruitmentGBUnited Kingdo
DISTRIBUTIONAL AND LOCAL LIMIT LAWS FOR A CLASS OF ITERATED MAPS THAT CONTRACT ON AVERAGE
Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.
BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700
Invariance principles for iterated maps that contract on average
We consider iterated function schemes that contract on average. Using a transfer operator approach, we prove a version of the almost sure invariance principle. This allows the system to be modelled by a Brownian motion, up to some error term. It follows that many classical statistical properties hold for such systems, such as the weak invariance principle and the law of the iterated logarithm
Transfer operators for contractive Markov systems and stochastic stability of the invariant measure
Cocycles in Hyperbolic Dynamics: Livsic Regularity Theorems and Applications to Stable Ergodicity
We give a brief summary of the results presented in this thesis together with some of the relevant background. We do not give complete definitions here of some of the required constructions in hyperbolic dynamics and Lie groups, but instead refer the reader either to the relevant chapter or to [KH]. Often, we will not state how smooth the various maps are assumed to be. Instead we just assume that everything is smooth enough to make sense. x1 Hyperbolic dynamical systems This thesis is primarily about hyperbolic dynamical systems. Here we give a brief summary of such systems and, in particular, relate them to Anosov systems and Smale's Axiom A. Let M be a compact Riemannian manifold and let OE be a diffeomorphism of M . A closed OE-invariant subset ae M is said to possess a hyperbolic splitting if the tangent bundle restricted to , T M , has a continuous splitting into two sub-bundles E s , E u for which there exist constants C ? 0, 2 (0; 1) such that kdOE n j E sk ..