Bowen Measure From Heteroclinic Points

We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces

RXTE observations of the dipping low-mass X-ray binary 4U 1624-49

We analyse ~ 360 ks of archival data from the Rossi X-Ray Timing Explorer (RXTE) of the 21 hr orbital period dipping low-mass X-ray binary 4U 1624-49. We find that outside the dips the tracks in the colour-colour and hardness-intensity diagrams (CDs and HIDs) are reminiscent of those of atoll sources in the middle and upper parts of the banana branch. The tracks show secular shifts up to ~ 10%. We study the power spectrum of 4U 1624-49 as a function of the position in the CD. This is the first time power spectra of this source are presented. No quasi-periodic oscillations (QPOs) are found. The power spectra are dominated by very low frequency noise (VLFN), characteristic for atoll sources in the banana state, and band limited noise (BLN) which is not reliably detected but may, uncharacteristically, strengthen and increase in frequency with spectral hardness. The VLFN fits to a power law, which becomes steeper when the source moves to the harder part of the CD. We conclude that 4U 1624-49 is an atoll source which in our observations is in the upper banana branch. Combining this with the high (0.5-0.7 L_Edd) luminosity, the long-term flux stability of the source as seen with the RXTE All-Sky Monitor (ASM), and with the fact that it is an X-ray dip source, we conclude that 4U 1624-49 is most likely a GX atoll source such as GX 3+1 and GX 9+9, but seen edge on.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in A&A. This version: a few typos correcte

Eliashberg's proof of Cerf's theorem

Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method.Comment: 32 page

RXTE Studies of Long-Term X-ray Spectral Variations in 4U 1820-30

We present the results of detailed spectral studies of the ultra-compact low mass X-ray binary (LMXB) 4U 1820-30 carried out with the Rossi X-ray Timing Explorer (RXTE) during 1996-7. 4U 1820-30 is an ``atoll'' source X-ray burster (XRB) located in the globular cluster NGC 6624. It is known to have an 11 minute binary period and a ~176 day modulation in its 2--12 keV flux. Observations were made with the PCA and HEXTE instruments on RXTE at roughly one-month intervals to sample this long-term period and study flux-related spectral changes. There are clear correlations between our fitted spectral parameters and both the broad-band (2--50 keV) flux and the position in the color-color diagram, as described by the parameter S_a introduced by Mendez et al. (1999). In addition, we find a strong correlation between the position in the color-color diagram and the frequencies of the kilohertz quasi-periodic oscillations (kHz QPOs) reported by Zhang et al. (1998). This lends further support to the notion that evidence for the last stable orbit in the accretion disk of 4U 1820-30 has been observed. For a model consisting of Comptonization of cool photons by hot electrons plus an additional blackbody component, we report an abrupt change in the spectral parameters at the same accretion rate at which the kHz QPOs disappear. For a model consisting of a multicolor disk blackbody plus a cut-off power law, we find that the inner disk radius reaches a minimum at the same accretion rate at which the kHz QPO frequency saturates, as expected if the disk reaches the last stable orbit. Both models face theoretical and observational problems when interpreted physically for this system.Comment: 39 pages, 11 figures, accepted to the Astrophysical Journa