A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

A max-type recursive model: some properties and open questions

We consider a simple max-type recursive model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux. Our interest is focused on the critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures.Comment: A version accepted to Charles Newman Festschrift (to appear by Springer

Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

Hierarchical pinning models, quadratic maps and quenched disorder

We consider a hierarchical model of polymer pinning in presence of quenched disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which can be re-interpreted as an infinite dimensional dynamical system with random initial condition (the disorder). It is defined through a recurrence relation for the law of a random variable {R_n}_{n=1,2,...}, which in absence of disorder (i.e., when the initial condition is degenerate) reduces to a particular case of the well-known Logistic Map. The large-n limit of the sequence of random variables 2^{-n} log R_n, a non-random quantity which is naturally interpreted as a free energy, plays a central role in our analysis. The model depends on a parameter alpha>0, related to the geometry of the hierarchical lattice, and has a phase transition in the sense that the free energy is positive if the expectation of R_0 is larger than a certain threshold value, and it is zero otherwise. It was conjectured by Derrida et al. (1992) that disorder is relevant (respectively, irrelevant or marginally relevant) if 1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an arbitrarily small amount of randomness in the initial condition modifies the critical point with respect to that of the pure (i.e., non-disordered) model if alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main result is a proof of these conjectures for the case alpha different from 1/2. We emphasize that for alpha>1/2 we find the correct scaling form (for weak disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab. Theory Rel. Field

Simultaneous multi-band detection of Low Surface Brightness galaxies with Markovian modelling

We present an algorithm for the detection of Low Surface Brightness (LSB) galaxies in images, called MARSIAA (MARkovian Software for Image Analysis in Astronomy), which is based on multi-scale Markovian modeling. MARSIAA can be applied simultaneously to different bands. It segments an image into a user-defined number of classes, according to their surface brightness and surroundings - typically, one or two classes contain the LSB structures. We have developed an algorithm, called DetectLSB, which allows the efficient identification of LSB galaxies from among the candidate sources selected by MARSIAA. To assess the robustness of our method, the method was applied to a set of 18 B and I band images (covering 1.3 square degrees in total) of the Virgo cluster. To further assess the completeness of the results of our method, both MARSIAA, SExtractor, and DetectLSB were applied to search for (i) mock Virgo LSB galaxies inserted into a set of deep Next Generation Virgo Survey (NGVS) gri-band subimages and (ii) Virgo LSB galaxies identified by eye in a full set of NGVS square degree gri images. MARSIAA/DetectLSB recovered ~20% more mock LSB galaxies and ~40% more LSB galaxies identified by eye than SExtractor/DetectLSB. With a 90% fraction of false positives from an entirely unsupervised pipeline, a completeness of 90% is reached for sources with r_e > 3" at a mean surface brightness level of mu_g=27.7 mag/arcsec^2 and a central surface brightness of mu^0 g=26.7 mag/arcsec^2. About 10% of the false positives are artifacts, the rest being background galaxies. We have found our method to be complementary to the application of matched filters and an optimized use of SExtractor, and to have the following advantages: it is scale-free, can be applied simultaneously to several bands, and is well adapted for crowded regions on the sky.Comment: 39 pages, 18 figures, accepted for publication in A

New Abundances for Old Stars - Atomic Diffusion at Work in NGC 6397

A homogeneous spectroscopic analysis of unevolved and evolved stars in the metal-poor globular cluster NGC 6397 with FLAMES-UVES reveals systematic trends of stellar surface abundances that are likely caused by atomic diffusion. This finding helps to understand, among other issues, why the lithium abundances of old halo stars are significantly lower than the abundance found to be produced shortly after the Big Bang.Comment: 8 pages, 7 colour figures, 1 table; can also be downloaded via http://www.eso.org/messenger

Thermodynamic Limit Of The Ginzburg-Landau Equations

We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in unbounded domain. This semiflow is proven to exist in dimension 1 and 2 for any parameter values of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some restrictions on the parameters but cover nevertheless some part of the Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]

Professional Concerns

In the contribution which follows, Collett B. Dilworth, Jr., of the English Department at East Carolina University, gets to the very heart of why literature is taught in schools. He broaches the question of how literary study relates to the basic skills, and he ties his rationale in with questions of accountability and its handmaiden, competency testing. Probably the heart of Dilworth\u27s argument is in his statement, The student of literature is not primarily looking for information, s/he is looking for experience