The Optical Gravitational Lensing Experiment. Small Amplitude Variable   Red Giants in the Magellanic Clouds
  We present analysis of the large sample of variable red giants from the Large and Small Magellanic Clouds detected during the second phase of the Optical Gravitational Lensing Experiment (OGLE-II) and supplemented with OGLE-III photometry. Comparing pulsation properties of detected objects we find that they constitute two groups with clearly distinct features. In this paper we analyze in detail small amplitude variable red giants (about 15400 and 3000 objects in the LMC and SMC, respectively). The vast majority of these objects are multi-periodic. At least 30% of them exhibit two modes closely spaced in the power spectrum, what likely indicates non-radial oscillations. About 50% exhibit additional so called Long Secondary Period.   To distinguish between AGB and RGB red giants we compare PL diagrams of multi-periodic red giants located above and below the tip of the Red Giant Branch (TRGB). The giants above the TRGB form four parallel ridges in the PL diagram. Among much more numerous sample of giants below the TRGB we find objects located on the low luminosity extensions of these ridges, but most of the stars are located on the ridges slightly shifted in logP. We interpret the former as the second ascent AGB red giants and the latter as the first ascent RGB objects. Thus, we empirically show that the pulsating red giants fainter than the TRGB are a mixture of RGB and AGB giants.   Finally, we compare the Petersen diagrams of the LMC, SMC and Galactic bulge variable red giants and find that they are basically identical indicating that the variable red giants in all these different stellar environments share similar pulsation properties. 
I. Soszynski, A. Udalski, M. Kubiak, M. Szymanski, G. Pietrzynski, K.   Zebrun, O. Szewczyk, L. Wyrzykowski