C1C^1-Generic Symplectic Diffeomorphisms: Partial Hyperbolicity and Zero Center Lyapunov Exponents

We prove that if $f$ is a $C^1$-generic symplectic diffeomorphism then the Oseledets splitting along almost every orbit is either trivial or partially hyperbolic. In addition, if $f$ is not Anosov then all the exponents in the center bundle vanish. This establishes in full a result announced by R. Ma\~{n}\'{e} in the ICM 1983. The main technical novelty is a probabilistic method for the construction of perturbations, using random walks.Comment: Final version. To appear in Journal of the Institute of Mathematics of Jussie

Closed orbits of a charge in a weakly exact magnetic field

We prove that for a weakly exact magnetic system on a closed connected Riemannian manifold, almost all energy levels contain a closed orbit. More precisely, we prove the following stronger statements. Let $(M,g)$ denote a closed connected Riemannian manifold and $\sigma$ a weakly exact 2-form. Let $\phi_{t}$ denote the magnetic flow determined by $\sigma$, and let $c$ denote the Mane critical value of the pair $(g,\sigma)$. We prove that if $k>c$, then for every non-trivial free homotopy class of loops on $M$ there exists a closed orbit with energy $k$ whose projection to $M$ belongs to that free homotopy class. We also prove that for almost all $k<c$ there exists a closed orbit with energy $k$ whose projection to $M$ is contractible. In particular, when $c=\infty$ this implies that almost every energy level has a contractible closed orbit. As a corollary we deduce that if $\sigma$ is not exact and $M$ has an amenable fundamental group (which implies $c=\infty$) then there exist contractible closed orbits on almost every energy level.Comment: 25 pages. v3 - minor corrections, this version to appear in PJ

Characterization of gas-rich galaxies from ALFALFA's survey data

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Josep Maria Solanes MajúaThis research work is the first statistical study of the properties of the galaxies included in the final data release (A-100) of the Arecibo Legacy Fast ALFA survey (ALFALFA). The recently completed ALFALFA survey constitutes a representative sample of the nearby Universe in the 21 cm line of the neutral Hidrogen (HI), with more than 30 000 extragalactic sources out to z 0:06. Its substantial overlap with wide-area surveys conducted at other wavelengths has been used to create a consistent multi-wavelength catalog of parameters for galaxies within about 250 Mpc (800 million light-years) from us. We have characterized the gas-rich galaxies by comparing their content of atomic hydrogen with several properties from the optical window ranging from intrinsic luminosities and colors to estimators of the morphology and structure. Our results corroborate earlier findings that there does not appear to be a significant population of optically dark but HI-rich galaxies and that most HI-rich galaxies are very blue, while we find that their colors and HI masses are more strongly correlated than previously suspected. In addition, we have (not just confirmed but) found a clearer decrement of the bar fraction with increasing HI content, an anti-correlation that is not explained by known trends for more massive (stellar) and redder disc galaxies to host more bars and have lower gas content

Hallado un incensario en Thuqaibah (Sharjah, Emiratos Árabes Unidos): interpretaciones de una forma singular en determinadas estructuras de la Edad del Hierro

For the seasons from 1994 in the United Arab Emirates, the Spanish team have greatly contributed to the knowledge of the Iron Age (1300-300 b. C.) in the Oman peninsula. Especially so far as the construction of mudbrick dwellings and the collection of water resources are concerned, and, of course, the consequent conclusions related to the way of life and subsistence of peoples from this period. The finding in recent years (2001-2005) of a construction with clear different shades with respect to the dwellings excavated in this sector, AM1-Thuqaibah, until today and the presence of some objects unknown till now in this area make us think we have a space reserved for something different from the daily life, although we can not at present state a clear hierarchical or even religious functionLas campañas llevadas a cabo por la misión española en los Emiratos Árabes Unidos desde el año 1994 han contribuido generosamente al conocimiento de la Edad del Hierro (1300-300 a.C.) en la península de Omán. En especial en lo tocante a la construcción de lugares de habitación en adobe y a la captación de recursos acuíferos, con las consiguientes conclusiones referidas al modo de vida y subsistencia de las gentes de este periodo. El hallazgo en los últimos años (2001-2005) de una construcción con claros matices diferenciadores respecto a los lugares de hábitat excavados en el sector AM1-Thuqaibah hasta el momento y la presencia de ciertos objetos hasta ahora desconocidos en el área nos hacen pensar que nos encontramos ante un espacio reservado a algo más que la existencia cotidiana, aunque no podamos por el momento afirmar una funcionalidad clara de tipo jerárquico o incluso religioso