SIMBAD references

The AAVSO lightcurve data of the irregularly pulsating star AC Herculis of the RV Tau class are analysed. The lightcurve is shown not to be compatible with a periodic, or even multiperiodic pulsation, even if allowance is made for evolution. Instead the best explanation is that the irregularly alternating cycles are a manifestation of low dimensional chaos. Our flow reconstruction suggests that the dynamics can be successfully embedded in 3 dimensions. Further, the (Lyapunov) fractal dimension of the underlying dynamic attractor is computed to be 2.05≲d_L≲2.45, independent of the dimension of the reconstruction space. It is smaller than the value of d_L≃3.1 found for the more irregular lightcurve of R Sct. From these results we are led to conclude that the lightcurve is likely to have been generated by a 3 dimensional dynamics, i.e. by 3 first order ODEs. In simpler language, it expresses the remarkable fact that the observational value at any time s(t_n) is a unique function h of the values at only three preceding observations, viz. s(t_n+1)=h(s(t_n),s(t_n–1),s(t_n–2)).