1,452 research outputs found
Rigidity of Holomorphic Collet-Eckmann Repellers
No full text. We prove rigidity results for a class of non-uniformly hyperbolic holomorphic maps: If a holomorphic Collet-Eckmann map f is topologically conjugate to a holomorphic map g, then the conjugacy can be improved to be quasiconformal. If there is only one critical point in the repeller, then g is Collet-Eckmann, too. 1. Introduction Collet-Eckmann maps of the interval were introduced by P. Collet and J.-P. Eckmann as a large class of non-uniformly expanding maps for which a probability absolutely continuous invariant measure exists. A theory of rational Collet-Eckmann maps was originated in [P2] and continued in [P3], [GS] and [PR]; see [PR] for a more detailed historical account. This paper is a continuation of [PR]. We consider repellers for holomorphic maps, without assuming the maps extend to rational maps. Consider a compact set X in the Riemann sphere C , together with a holomorphic map f : U ! C with f(X) = X, where U is a neighbourhood of X. We call the pair (X; f) a holomorp..
Fallbeispiele. Exemplarische Dokumentation konkreter Praxisverläufe.
No full textDemmer C. Fallbeispiele. Exemplarische Dokumentation konkreter Praxisverläufe. In: Eckmann T, Demmer C (H), eds. "Jenseits des Alltags" - Anleitung zum sozialästhetischen Handeln in der pädagogischen Praxis. Bochum: Projektverlag; 2009: 113-428
Donegal 2007: Zusammenfassung und Schlussbericht des Evaluierungsprojekts "Jenseits des Alltags".
No full textDemmer C. Donegal 2007: Zusammenfassung und Schlussbericht des Evaluierungsprojekts "Jenseits des Alltags". In: Eckmann T, Demmer C (H), eds. "Jenseits des Alltags" - Anleitung zum sozialästhetischen Handeln in der pädagogischen Praxis. Bochum: Projektverlag; 2009: 78-103
"Jenseits des Alltags" - Anleitung zum sozialästhetischen Handeln in der pädagogischen Praxis.
No full textDemmer C, Eckmann T, eds. "Jenseits des Alltags" - Anleitung zum sozialästhetischen Handeln in der pädagogischen Praxis. Bochum und Freiburg: Projektverlag; 2009
Porosity Of Collet-Eckmann Julia Sets
No full text. We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2. 1. Introduction Let f : b C ! b C be a rational map. Then f is said to satisfy the Collet-Eckmann condition if there are constants C ? 0 and ? 1 such that (CE) j(f n ) 0 (f(c))j C n for all n and all critical points c 2 J(f) of f whose forward orbit does not meet another critical point (J(f) stands for the Julia set of f ). Here and in what follows derivatives and distances are always with respect to the spherical metric of b C ; unless stated otherwise. A set E ae b C is called mean porous if there are constants p 1 ! 1 and p 2 ? 0 such that for each z 2 E the following holds: There is an increasing sequence n j of integers and points z j with dist(z; z j ) 2 \Gamman j such that n j ! p 1 j and dist(z j ; E) ? ..
Porosity of Collet-Eckmann Julia sets
No full textAbstract. We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2
When to switch to an oral treatment and/or to discharge a patient with skin and soft tissue infections
No full textPurpose of review Skin and soft tissue infections prevalence is increasing and represent a frequent cause of hospital admission. New guidelines have become available in order to better define these infections and their response to antimicrobial treatment. Gram-positive bacteria, in particular Staphylococcus aureus, remain the most frequently isolated pathogens in skin and soft tissue infections. To treat complicated forms and infections caused by drug-resistant bacteria, hospital admission and administration of intravenous antibiotics are often required, impacting on healthcare costs and patients' morbidity. Recent findings New therapeutic options offer efficacy against drug-resistant Gram-positive bacteria as well as potential to favor early patients' discharge, including the possibility for intravenous to oral switch and infrequent drug administration because of prolonged drug half-life. Although data from real-world studies on new antimicrobials is awaited, clinicians need clear direction on how to optimize the treatment of skin and soft tissue infections in order to avoid prolonged hospitalizations and extra costs. Early assessment of patient's clinical conditions and response to treatment appear useful in order to facilitate patients' discharge. Summary We have reported the evidence for early intravenous to oral switch and early hospital discharge for patients with skin and soft tissue infections. New therapeutic options that represent promising tools in promoting an optimized management of these infections have also been reviewed
Topological invariance of the Collet-Eckmann property for S-unimodal maps
No full textAbstract. We prove that if f , g are smooth unimodal maps of the interval with negative Schwarzian derivative, conjugated by a homeomorphism of the interval, and f is Collet-Eckmann, then so is g
On the Pointwise Dimension of Hyperbolic Measures: a Proof of the Eckmann-Ruelle Conjecture
No full textWe prove the long-standing Eckmann--Ruelle conjecture in dimension theory of smooth dynamical systems. We show that the pointwise dimension exists almost everywhere with respect to a compactly supported Borel probability measure with non-zero Lyapunov exponents, invariant under a C 1+ff diffeomorphism of a smooth Riemannian manifold
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