The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

A birational mapping with a strange attractor: Post critical set and covariant curves

We consider some two-dimensional birational transformations. One of them is a birational deformation of the H\'enon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic two-form. One may have also an infinite post critical set yielding a covariant curve which is not algebraic (transcendent). For two of the birational mappings considered, the post critical set is not infinite and we claim that there is no algebraic covariant curve and no preserved meromorphic two-form. For these two mappings with non infinite post critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.Comment: 26 pages, 11 figure

First light of the VLT planet finder SPHERE. I. Detection and characterization of the sub-stellar companion GJ 758 B

GJ758 B is a brown dwarf companion to a nearby (15.76 pc) solar-type, metal-rich (M/H = +0.2 dex) main-sequence star (G9V) that was discovered with Subaru/HiCIAO in 2009. From previous studies, it has drawn attention as being the coldest (~600K) companion ever directly imaged around a neighboring star. We present new high-contrast data obtained during the commissioning of the SPHERE instrument at the VLT. The data was obtained in Y-, J-, H-, and Ks-bands with the dual-band imaging (DBI) mode of IRDIS, providing a broad coverage of the full near-infrared (near-IR) range at higher contrast and better spectral sampling than previously reported. In this new set of high-quality data, we report the re-detection of the companion, as well as the first detection of a new candidate closer-in to the star. We use the new 8 photometric points for an extended comparison of GJ758 B with empirical objects and 4 families of atmospheric models. From comparison to empirical object, we estimate a T8 spectral type, but none of the comparison object can accurately represent the observed near-IR fluxes of GJ758 B. From comparison to atmospheric models, we attribute a Teff = 600K $\pm$ 100K, but we find that no atmospheric model can adequately fit all the fluxes of GJ758 B. The photometry of the new candidate companion is broadly consistent with L-type objects, but a second epoch with improved photometry is necessary to clarify its status. The new astrometry of GJ758 B shows a significant proper motion since the last epoch. We use this result to improve the determination of the orbital characteristics using two fitting approaches, Least-Square Monte Carlo and Markov Chain Monte Carlo. Finally, we analyze the sensitivity of our data to additional closer-in companions and reject the possibility of other massive brown dwarf companions down to 4-5 AU. [abridged]Comment: 20 pages, 15 figures. Accepted for publication in A&

SPICES: Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems

SPICES (Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems) is a five-year M-class mission proposed to ESA Cosmic Vision. Its purpose is to image and characterize long-period extrasolar planets and circumstellar disks in the visible (450 - 900 nm) at a spectral resolution of about 40 using both spectroscopy and polarimetry. By 2020/22, present and near-term instruments will have found several tens of planets that SPICES will be able to observe and study in detail. Equipped with a 1.5 m telescope, SPICES can preferentially access exoplanets located at several AUs (0.5-10 AU) from nearby stars ($<$25 pc) with masses ranging from a few Jupiter masses to Super Earths ($\sim$2 Earth radii, $\sim$10 M$_{\oplus}$) as well as circumstellar disks as faint as a few times the zodiacal light in the Solar System

First light of the VLT planet finder SPHERE. II. The physical properties and the architecture of the young systems PZ Tel and HD 1160 revisited

[Abridged] Context. The young systems PZ Tel and HD 1160, hosting known low-mass companions, were observed during the commissioning of the new planet finder SPHERE with several imaging and spectroscopic modes. Aims. We aim to refine the physical properties and architecture of both systems. Methods. We use SPHERE commissioning data and REM observations, as well as literature and unpublished data from VLT/SINFONI, VLT/NaCo, Gemini/NICI, and Keck/NIRC2. Results. We derive new photometry and confirm the nearly daily photometric variability of PZ Tel A. Using literature data spanning 38 yr, we show that the star also exhibits a long-term variability trend. The 0.63-3.8 mic SED of PZ Tel B allows us to revise its properties: spectral type M7+/-1, Teff=2700+/-100 K, log(g)<4.5 dex, log(L/L_Sun)=-2.51+/-0.10 dex, and mass 38-72 MJ. The 1-3.8 mic SED of HD 1160 B suggests a massive brown dwarf or a low-mass star with spectral type M5.5-7.0, Teff=3000+/-100 K, [M/H]=-0.5-0.0 dex, log(L/L_Sun)=-2.81+/-0.10 dex, and mass 39-168 MJ. We confirm the deceleration and high eccentricity (e>0.66) of PZ Tel B. For e<0.9, the inclination, longitude of the ascending node, and time of periastron passage are well constrained. The system is seen close to an edge-on geometry. We reject other brown dwarf candidates outside 0.25" for both systems, and massive giant planets (>4 MJ) outside 0.5" for the PZ Tel system. We also show that K1-K2 color can be used with YJH low-resolution spectra to identify young L-type companions, provided high photometric accuracy (<0.05 mag) is achieved. Conclusions. SPHERE opens new horizons in the study of young brown dwarfs and giant exoplanets thanks to high-contrast imaging capabilities at optical and near-infrared wavelengths, as well as high signal-to-noise spectroscopy in the near-infrared from low (R~30-50) to medium resolutions (R~350).Comment: 25 pages, 23 figures, accepted for publication in A&A on Oct. 13th, 2015; version including language editing. Typo on co-author name on astroph page corrected, manuscript unchange