Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

The strange case of Dr Jekyll and Mr Hyde.

EL DR. JEKYLL Y MR. HYDE evoca el lado oscuro de la condición humana e ilumina mundos ocultos bajo la delgada capa de las convenciones sociales, transmitiendo al lector la sensación de horror que suscita el descubrimiento de lo abominable dentro de la realidad cotidiana. Su soberbia calidad literaria, su perfección formal y la economía de medios de su argumento han hecho de este admirable relato un clásico de la novela corta que admite varias lecturas no contradictorias entre sí: desde la entrega al eficaz suspense de la trama, a su interpretación como una fábula sobre la ambigüedad moral del hombre, escenario para la perpetua lucha entre el bien y el mal.

Anna In-Between: Caribbean and not Caribbean: attachment, loss and strange Longing: a conversation with Elizabeth Nunez

Presents an interview with Elizabeth Nunez, author and professor. Nunez discusses the issues on migration, family, and intimacy which are the topics of her novel "Anna In-Between." She explains the demands of the publishing industry that cast a shadow in the world of the novel and the real world of Caribbean writers. This interview was translated by Maria Lusia Ruiz.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Existence of pullback attractors for pullback asymptotically compact processes

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) (i) An autonomous evolution process which is bounded, dissipative and asymptotically compact has a global attractor. (ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non-autonomous evolution processes. An application to damped wave problem with non-autonomous damping is considered. (C) 2009 Elsevier Ltd. All rights reserved.