Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type

We describe the topological behavior of typical orbits of complex quadratic polynomials P_alpha(z)=e^{2\pi i alpha} z+z^2, with alpha of high return type. Here we prove that for such Brjuno values of alpha the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then combining with Part I of this work, we show that the limit set of the orbit of a typical point in the Julia set is equal to the closure of the critical orbit.Comment: 38 pages, 5 figures; fixed the issues with processing the figure

Newton's method and Baker domains

We show that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic functions without Baker domains. We also show that there exists an entire function f with exactly one zero for which the complement of the immediate attracting basin has at least two components and contains no invariant Baker domains of N. The second result answers a question of J. Rueckert and D. Schleicher while the first one gives a partial answer to a question of X. Buff.Comment: 6 page

Classification of Complex Polynomial Vector Fields in One Complex Variable

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference Equations and Application

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page

Some examples of Baker domains

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others.Comment: 13 page

Affecting Rhomboid-3 Function Causes a Dilated Heart in Adult Drosophila

Drosophila is a well recognized model of several human diseases, and recent investigations have demonstrated that Drosophila can be used as a model of human heart failure. Previously, we described that optical coherence tomography (OCT) can be used to rapidly examine the cardiac function in adult, awake flies. This technique provides images that are similar to echocardiography in humans, and therefore we postulated that this approach could be combined with the vast resources that are available in the fly community to identify new mutants that have abnormal heart function, a hallmark of certain cardiovascular diseases. Using OCT to examine the cardiac function in adult Drosophila from a set of molecularly-defined genomic deficiencies from the DrosDel and Exelixis collections, we identified an abnormally enlarged cardiac chamber in a series of deficiency mutants spanning the rhomboid 3 locus. Rhomboid 3 is a member of a highly conserved family of intramembrane serine proteases and processes Spitz, an epidermal growth factor (EGF)–like ligand. Using multiple approaches based on the examination of deficiency stocks, a series of mutants in the rhomboid-Spitz–EGF receptor pathway, and cardiac-specific transgenic rescue or dominant-negative repression of EGFR, we demonstrate that rhomboid 3 mediated activation of the EGF receptor pathway is necessary for proper adult cardiac function. The importance of EGF receptor signaling in the adult Drosophila heart underscores the concept that evolutionarily conserved signaling mechanisms are required to maintain normal myocardial function. Interestingly, prior work showing the inhibition of ErbB2, a member of the EGF receptor family, in transgenic knock-out mice or individuals that received herceptin chemotherapy is associated with the development of dilated cardiomyopathy. Our results, in conjunction with the demonstration that altered ErbB2 signaling underlies certain forms of mammalian cardiomyopathy, suggest that an evolutionarily conserved signaling mechanism may be necessary to maintain post-developmental cardiac function

Past, Present, and Future X-Ray and Gamma-Ray Missions

X- and -ray astronomy began in the early sixties of the last century with balloons flights, sounding rocket experiment and satellites. Long before space satellite detected X- and -rays emitted by cosmic sources, scientists had known that the Universe should be producing these photons. In this chapter we provided an overview of past and present missions that has made the X- and -ray astronomy an integral part of astronomical research, and prospects of future developments