Li-Yorke Chaos for Composition Operators on LpL^p-Spaces

Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more useful characterizations of Li-Yorke chaos can be given in the special setting of composition operators on $L^p$ spaces. As a consequence we obtain a simple characterization of weighted shifts which are Li-Yorke chaotic. We give numerous examples to show that our results are sharp

Cosmographic constraints on a class of Palatini f(R) gravity

Modified gravity, known as $f(R)$ gravity, has presently been applied to Cosmology as a realistic alternative to dark energy. For this kind of gravity the expansion of the Universe may accelerate while containing only baryonic and cold dark matter. The aim of the present investigation is to place cosmographic constraints on the class of theories of the form $f(R)=R - \alpha/R^n$ within the Palatini approach. Although extensively discussed in recent literature and confronted with several observational data sets, cosmological tests are indeed inconclusive about the true signal of $n$ in this class of theories. This is particularly important to define which kind of corrections (infra-red or high-energy) to general relativity this class of theory indeed represent. We shed some light on this question by examining the evolution of the deceleration parameter $q(z)$ for these theories. We find that for a large range of $\alpha$, models based on $f(R) = R - \alpha/R^{n}$ gravity in the Palatini approach can only have positive values for $n$, placing thus a broad restriction on this class of gravity.Comment: 4 pages, 2 figures, Latex, Submitte

Type II Seesaw and a Gauge Model for the Bimaximal Mixing Explanation of Neutrino Puzzles

We present a gauge model for the bimaximal mixing pattern among the neutrinos that explains both the atmospheric and solar neutrino data via large angle vacuum oscillation among the three known neutrinos. The model does not include righthanded neutrinos but additional Higgs triplets which acquire naturally small vev's due to the type II seesaw mechanism. A combination of global $L_e-L_{\mu}-L_{\tau}$ and $S_3$ symmetries constrain the mass matrix for both charged leptons and neutrinos in such a way that the bimaximal pattern emerges naturally at the tree level and needed splittings among neutrinos at the one loop level. This model predicts observable branching ratios for $\tau\to \mu \mu\mu$, which could be used to test it.Comment: Latex file, 8 pages, five figures include