Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems

For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to an extreme value distribution, and obtain estimates on the rate of convergence. We show that our results are applicable to a range of examples, and include new results for Lorenz maps, certain partially hyperbolic systems, and non-uniformly expanding systems with sub-exponential decay of correlations. For applications where analytic results are not readily available we show how to estimate the rate of convergence to an extreme value distribution based upon numerical information of the quantitative recurrence statistics. We envisage that such information will lead to more efficient statistical parameter estimation schemes based upon the block-maxima method.Comment: This article is a revision of the previous article titled: "On the convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems." Relative to this older version, the revised article includes new and up to date results and developments (based upon recent advances in the field

Symmetries in the Lorenz-96 model

The Lorenz-96 model is widely used as a test model for various applications, such as data assimilation methods. This symmetric model has the forcing $F\in\mathbb{R}$ and the dimension $n\in\mathbb{N}$ as parameters and is $\mathbb{Z}_n$ equivariant. In this paper, we unravel its dynamics for $F<0$ using equivariant bifurcation theory. Symmetry gives rise to invariant subspaces, that play an important role in this model. We exploit them in order to generalise results from a low dimension to all multiples of that dimension. We discuss symmetry for periodic orbits as well. Our analysis leads to proofs of the existence of pitchfork bifurcations for $F<0$ in specific dimensions $n$: In all even dimensions, the equilibrium $(F,\ldots,F)$ exhibits a supercritical pitchfork bifurcation. In dimensions $n=4k$, $k\in\mathbb{N}$, a second supercritical pitchfork bifurcation occurs simultaneously for both equilibria originating from the previous one. Furthermore, numerical observations reveal that in dimension $n=2^qp$, where $q\in\mathbb{N}\cup\{0\}$ and $p$ is odd, there is a finite cascade of exactly $q$ subsequent pitchfork bifurcations, whose bifurcation values are independent of $n$. This structure is discussed and interpreted in light of the symmetries of the model.Comment: 31 pages, 9 figures and 3 table

La traduzione letteraria turco-catalano

Quando si considera la relazione letteraria stabilita tra il turco e il catalano per mezzo della traduzione appare con evidenza la scarsità dei frutti di questa. Effettivamente, esistono solo due opere tradotte dal catalano al turco mentre, in lingua catalana, troviamo alcune poesie tradotte dal turco. Le altre pochissime opere tradotte sono state trasferite da una lingua intermedia. Si nota che nelle traduzioni dal catalano al turco si utilizza generalmente la versione spagnola intermedia, invece in quelle catalane si preferisce più spesso l'inglese. Attraverso una panoramica sulla storia della traduzione nella tradizione letteraria turca e catalana, questo articolo aspira a spiegare le possibili ragioni della mancanza di opere tradotte dal catalano al turco o viceversa, soffermandosi sugli orientamenti particolari dell'attività traduttiva delle due lingue.When the literary relation built between the Catalan and the Turkish through translation are taken into consideration, the scarcity of the translated works stands out as particularly important. As a direct translation between two languages, there are only two literary works translated from Catalan into Turkish and few poems translated from Turkish into Catalan. In the translations from either language, a third language is largely used as an intermediary. While Turkish translations from Catalan are mostly done through the mediation of Spanish, English comes to be the largely preferred intermediary language in the translations from Turkish into Catalan. By discussing the history of translation in both literary traditions, this paper aims at rethinking the possible reasons behind such a scarcity by focusing on the distinguishing orientations of translation in both languages

VLBI astrometry of two millisecond pulsars

We present astrometric results on two millisecond pulsars, PSR B1257+12 and PSR J1022+1001, as carried out through VLBI. For PSR B1257+12, a model-independent distance of $710_{\rm -38}^{\rm +43}$ pc and proper motion of ($\mu_{\rm \alpha}=46.44\pm0.08$ mas/yr, $\mu_{\rm \delta}=-84.87\pm0.32$ mas/yr) were obtained from 5 epochs of VLBA and 4 epochs of EVN observations, spanning about 2 years. The two dimensional proper motion of PSR J1022+1001 ($\mu_{\rm \alpha} \sim -10.13$ mas/yr, $\mu_{\delta} \sim 16.89$ mas/yr) was also estimated, using 3 epochs of EVN observations. Based on our results, the X-ray efficiency of PSR B1257+12 should be in the same range as other millisecond pulsars, and not as low as previously thought.Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 3 page

Searching for low mass objects around nearby dMe radio stars

Nearby M-dwarfs are best suited for searches of low mass companions. VLBI phase-referencing observations with sensitive telescopes are able to detect radio star flux-densities of tenths of mJy as well as to position the star on the sky with submilliarcsecond precision. We have initiated a long-term observational program, using EVN telescopes in combination with NASA DSN dishes, to revisit the kinematics of nearby, single M dwarfs. The precision of the astrometry allows us to search for possible companions with masses down to 1 Jupiter mass. In this contribution we report preliminary results of the first observation epochs, in which we could detect some of the radio stars included in our program.Comment: Proceedings of the 6th European VLBI Network Symposium, Ros E., Porcas R.W., Lobanov A.P., & Zensus J.A. (eds.), MPIfR, Bonn, Germany, p. 255-258 (2002). 4 pages, 3 figures, needs evn2002.cl

A Global 86GHz VLBI Survey of Compact Radio Sources

We present results from a large 86GHz global VLBI survey of compact radio sources. The main goal of the survey is to increase by factors of 3--5 the total number of objects accessible for future 3-mm VLBI imaging. The survey observations reach the baseline sensitivity of 0.1Jy and image sensitivity of better than 10 mJy/beam. The total of 127 compact radio sources have been observed. The observations have yielded images for 109 sources, extending the database of the sources imaged at 86GHz with VLBI observation by a factor of 5, and only 6 sources have not been detected. The remaining 12 objects have been detected but could not be imaged due to insufficient closure phase information. Radio galaxies are less compact than quasars and BL Lacs on sub-milliarcsecond scale. Flux densities and sizes of core and jet components of all imaged sources have been estimated using Gaussian model fitting. From these measurements, brightness temperatures have been calculated, taking into account resolution limits of the data. The cores of 70% of the imaged sources are resolved. The core brightness temperatures of the sources peak at $\sim 10^{11}$ K and only 1% have brightness temperatures higher than $10^{12}$ K. Cores of Intraday Variable (IDV) sources are smaller in angular size than non-IDV sources, and so yield higher brightness temperatures.Comment: 72 pages, 12 figures, accepted for publication in the Astronomical Journa

Wave propagation in the Lorenz-96 model

In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter <i>n</i> and the forcing parameter <i>F</i>. For <i>F</i> &gt; 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with <i>n</i>, but its period tends to a finite limit as <i>n</i> → ∞. For <i>F</i> &lt; 0 and odd <i>n</i>, the first bifurcation is again a supercritical Hopf bifurcation, but in this case the period of the traveling wave also grows linearly with <i>n</i>. For <i>F</i> &lt; 0 and even <i>n</i>, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether <i>n</i> has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing <i>n</i> by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values <i>n</i> and <i>F</i>

Spectral Properties of the Core and the VLBI-Jets of Cygnus A

We present a detailed VLBI study of the spectral properties of the inner core region of the radio galaxy Cygnus A at 5 GHz, 15 GHz, 22 GHz, 43 GHz and 86 GHz. Our observations include an epoch using phase-referencing at 15 GHz and 22 GHz and the first successful VLBI observations of Cygnus A at 86 GHz. We find a pronounced two-sided jet structure, with a steep spectrum along the jet and an inverted spectrum towards the counter-jet. The inverted spectrum and the frequency-dependent jet-to-counter-jet ratio suggest that the inner counter-jet is covered by a circum-nuclear absorber as it is proposed by the unified scheme.Comment: 2 pages, 2 figures, Proceedings of the 7th EVN Symposium held in Toledo, Spain in October 2004, needs evn2004.cl