2005ApJ...635..527J

A nonlinear time series analysis is performed on light intensity data for the variable DB white dwarf PG 1351+489. The data were collected during the XCov12 campaign of the Whole Earth Telescope. Two data sets integrated to 30 and 10 s, taken at different times during the campaign, were analyzed. The power spectrum of PG 1351+489 is broadband, with a dominant fundamental frequency f₀, and its harmonics, subharmonics, and other lower amplitude peaks. Our time delay phase-space portrait in 3 dimensions is a rhombohedral shape wrapped around a torus with triangular projections. This differs from earlier reports of a more circular two-dimensional representation. We show that the difference is due to binning and subsequent filtering in the earlier work. A circular phase-space portrait is obtained if only the fundamental frequency is used, the reconstruction subsequently growing in complexity as more and more of the power spectrum is included. Poincaré section return times for the 30 s integrated data correspond to the fundamental period. For the 10 s integrated data, other return times are observed. These are shown to be due to dynamical resetting. An example of dynamical resetting on a theoretical model is given. Since resetting takes the phase-space point off the trajectory, locally projective nonlinear noise reduction was used. Locally projective nonlinear noise reduction results in lower white noise by a factor of ∼50. Thus, three more harmonics of the fundamental frequency f₀, four more (n+0.47)f₀subharmonics, and at least 12 other peaks are identified.