Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

On conformal measures and harmonic functions for group extensions

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.Comment: To appear in Proceedings of "New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

Magnetic fields of opposite polarity in sunspot penumbrae

Context. A significant part of the penumbral magnetic field returns below the surface in the very deep photosphere. For lines in the visible, a large portion of this return field can only be detected indirectly by studying its imprints on strongly asymmetric and three-lobed Stokes V profiles. Infrared lines probe a narrow layer in the very deep photosphere, providing the possibility of directly measuring the orientation of magnetic fields close to the solar surface. Aims. We study the topology of the penumbral magnetic field in the lower photosphere, focusing on regions where it returns below the surface. Methods. We analyzed 71 spectropolarimetric datasets from Hinode and from the GREGOR infrared spectrograph. We inferred the quality and polarimetric accuracy of the infrared data after applying several reduction steps. Techniques of spectral inversion and forward synthesis were used to test the detection algorithm. We compared the morphology and the fractional penumbral area covered by reversed-polarity and three-lobed Stokes V profiles for sunspots at disk center. We determined the amount of reversed-polarity and three-lobed Stokes V profiles in visible and infrared data of sunspots at various heliocentric angles. From the results, we computed center-to-limb variation curves, which were interpreted in the context of existing penumbral models. Results. Observations in visible and near-infrared spectral lines yield a significant difference in the penumbral area covered by magnetic fields of opposite polarity. In the infrared, the number of reversed-polarity Stokes V profiles is smaller by a factor of two than in the visible. For three-lobed Stokes V profiles the numbers differ by up to an order of magnitude.Comment: 11 pages 10 figures plus appendix (2 pages 3 figures). Accepted as part of the A&A special issue on the GREGOR solar telescop

The GREGOR Fabry-P\'erot Interferometer

The GREGOR Fabry-P\'erot Interferometer (GFPI) is one of three first-light instruments of the German 1.5-meter GREGOR solar telescope at the Observatorio del Teide, Tenerife, Spain. The GFPI uses two tunable etalons in collimated mounting. Thanks to its large-format, high-cadence CCD detectors with sophisticated computer hard- and software it is capable of scanning spectral lines with a cadence that is sufficient to capture the dynamic evolution of the solar atmosphere. The field-of-view (FOV) of 50" x 38" is well suited for quiet Sun and sunspot observations. However, in the vector spectropolarimetric mode the FOV reduces to 25" x 38". The spectral coverage in the spectroscopic mode extends from 530-860 nm with a theoretical spectral resolution R of about 250,000, whereas in the vector spectropolarimetric mode the wavelength range is at present limited to 580-660 nm. The combination of fast narrow-band imaging and post-factum image restoration has the potential for discovery science concerning the dynamic Sun and its magnetic field at spatial scales down to about 50 km on the solar surface.Comment: 14 pages, 17 figures, 4 tables; pre-print of AN 333, p.880-893, 2012 (AN special issue to GREGOR

Spectropolarimetric observations of an arch filament system with the GREGOR solar telescope

Arch filament systems occur in active sunspot groups, where a fibril structure connects areas of opposite magnetic polarity, in contrast to active region filaments that follow the polarity inversion line. We used the GREGOR Infrared Spectrograph (GRIS) to obtain the full Stokes vector in the spectral lines Si I 1082.7 nm, He I 1083.0 nm, and Ca I 1083.9 nm. We focus on the near-infrared calcium line to investigate the photospheric magnetic field and velocities, and use the line core intensities and velocities of the helium line to study the chromospheric plasma. The individual fibrils of the arch filament system connect the sunspot with patches of magnetic polarity opposite to that of the spot. These patches do not necessarily coincide with pores, where the magnetic field is strongest. Instead, areas are preferred not far from the polarity inversion line. These areas exhibit photospheric downflows of moderate velocity, but significantly higher downflows of up to 30 km/s in the chromospheric helium line. Our findings can be explained with new emerging flux where the matter flows downward along the fieldlines of rising flux tubes, in agreement with earlier results.Comment: Proceedings 12th Potsdam Thinkshop to appear in Astronomische Nachrichte

Inflationary Reheating in Grand Unified Theories

Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) What is the nature of chaotic reheating after inflation, and (2) How is reheating sensitive to the mass spectrum of these theories ? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances non-thermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which non-thermal destabilsation of discrete symmetries occurs at reheating.Comment: 4 pages, 5 ps figures - 1 colour, Revtex. Further (colour & 3-D) figures available from http://www.sissa.it/~bassett/reheating/ . Matched to version to appear in Phys. Rev. let