A New Spectrum for Nonlinear Operators in Banach Spaces

Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we define a subset sigma(f,p) of K, called spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in the linear case. More generally, we show that sigma(f,p) is always closed and, when f is C^1, coincides with the spectrum sigma(f'(p)) of the Frechet derivative of f at p. Some applications to bifurcation theory are given and some peculiar examples of spectra are provided.Comment: 23 pages, 3 figure

First human isolate of Salmonella enterica serotype enteritidis harboring bla CTX-M-14in South America

We studied a clinical isolate of Salmonella enterica serotype Enteritidis showing resistance to oxyiminocephalosporins. PCR analysis confirmed the presence of bla CTX-M-14 linked to IS903 in a 95-kb IncI1 conjugative plasmid. Such a plasmid is maintained on account of the presence of a pndAC addiction system. Multilocus sequence typing (MLST) analysis indicated that the strain belongs to ST11. This is the first report of bla CTX-M-14 in Salmonella Enteritidis of human origin in South America. Copyright © 2012, American Society for Microbiology. All Rights Reserved.CSIC (Comisión Sectorial de Investigación Científica, Uruguay); European Community (FP7-HEALTH-2007-223431); Ministerio de Ciencia e Innovación/Programa Bio-Fundamental (BFU2009-09200)Peer Reviewe

Equivariant degree for Abelian actions. Part III: orthogonal maps

The main goal of this paper is to define an equivariant degree theory for orthogonal maps. We apply our degree to study of bifurcations and existence of solutions of equivariant nonlinear problems

Equivariant degree theory

This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the theory and applications of this degree in a self-contained presentation starting with only elementary facts. The first chapter explains the basic tools of representation theory, homotopy theory and differential equations needed in the text. Then the degree is defined and its main abstract properties are derived. The next part is devoted to the study of equivariant homotopy groups of spheres and to the classification of equivariant maps in the case of abelian actions. These groups are explicitely computed and the effects of symmetry breaking, products and composition are thorougly studied. The last part deals with computations of the equivariant index of an isolated orbit and of an isolated loop of stationary points. Here differential equations in a variety of situations are considered: symmetry breaking, forcing, period doubling, twisted orbits, first integrals, gradients etc. Periodic solutions of Hamiltonian systems, in particular spring-pendulum systems, are studied as well as Hopf bifurcation for all these situations