Optical observations of 23 distant Jupiter Family Comets, including 36P/Whipple at multiple phase angles

We present photometry on 23 Jupiter Family Comets (JFCs) observed at large heliocentric distance, primarily using the 2.5-m Isaac Newton Telescope (INT). Snapshot images were taken of 17 comets, of which five were not detected, three were active and nine were unresolved and apparently inactive. These include 103P/Hartley 2, the target of the NASA Deep Impact extended mission, EPOXI. For six comets we obtained time-series photometry and use this to constrain the shape and rotation period of these nuclei. The data are not of sufficient quantity or quality to measure precise rotation periods, but the time-series do allow us to measure accurate effective radii and surface colours. Of the comets observed over an extended period, 40P/Väisälä 1, 47P/Ashbrook-Jackson and P/2004 H2 (Larsen) showed faint activity which limited the study of the nucleus. Light curves for 94P/Russell 4 and 121P/Shoemaker-Holt 2 reveal rotation periods of around 33 and 10h, respectively, although in both cases these are not unique solutions. 94P was observed to have a large range in magnitudes implying that it is one of the most elongated nuclei known, with an axial ratio a/b >= 3. 36P/Whipple was observed at five different epochs, with the INT and ESO's 3.6-m NTT, primarily in an attempt to confirm the preliminary short rotation period apparent in the first data set. The combined data set shows that the rotation period is actually longer than 24h. A measurement of the phase function of 36P's nucleus gives a relatively steep ß = 0.060 +/- 0.019. Finally, we discuss the distribution of surface colours observed in JFC nuclei, and show that it is possible to trace the evolution of colours from the Kuiper Belt Object (KBO) population to the JFC population by applying a `dereddening' function to the KBO colour distribution.

Resonances of the cusp family

We study a family of chaotic maps with limit cases-the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius-Perron operator in different function spaces including spaces of analytical functions and study numerically the eigenvalues and eigenfunctions.