Intrinsically localized chaos in discrete nonlinear extended systems

The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.Comment: 6 pages, 6 figures, to appear in Europhysics Letter

Black holes in extended gravity theories in Palatini formalism

We consider several physical scenarios where black holes within classical gravity theories including $R^2$ and Ricci-squared corrections and formulated \`a la Palatini can be analytically studied.Comment: 4 pages, contribution to the "Spanish Relativity Meeting in Portugal 2012 (Progress in Mathematical Relativity, Gravitation and Cosmology)", Springer Proceedings in Mathematics (to appear