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By J. R. Buchler, J. M. Perdang, E. A. Spiegel (auth.), J. R. Buchler, J. M. Perdang, E. A. Spiegel (eds.)

The according to iod of an oscillator tells us a lot approximately its constitution. J. J. Thomson's deduction particle with the e/rn of an electron was once within the atom is likely to be the main beautiful example. For us, the deduction of the suggest density of a celebrity from its oscillation interval is one other vital instance. What then do we deduce approximately an oscillator that's not periodic? If there are a number of frequencies or if the habit is chaotic, may possibly we now not wish to profit much more gentle important data approximately its workings? the hot growth within the idea of dynamical platforms, relatively within the elucidat ion of the character of chaos, makes it look moderate to invite this now. this is often an account of a few of the happenings of a workshop at which this query used to be raised and mentioned. ~iTe have been inc0rested in seeing ways that the current realizing of chaos could consultant astrophysical modelling and the translation of observations. yet we didn't try and cover that we have been additionally attracted to chaos itself, and that made for a delightful rapport among the chaoticists and astrophysicists on the assembly. now we have numerous introductory papers on chaos in those lawsuits, fairly at the research of information from platforms that could be suspected of chaotic habit. The papers of Geisel, Grassberger and Guckenheimer introduce the methods of characterizing chaos and Perdang illustrates how a few of these rules might be positioned into perform in specific cases.

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I 1977 ...... 5 .. 'b -30 +Velocity ~~ -40 .. o o ~~ • o o , 1978 . 4 -20 -20 -30 -40 . 5 . .... ..... 1979 -20 -30 -40 Fig. 7. The irregular variabil ity of 89 Her (Fernie 1981) • HD 161796 o 20 00 60 80 DAYS FROM MAX Fig. 8. Mode switching in HD 161796 (Fernie 1983). J. PERDANG 30 1978, but continued showing noisy fluctuations; in 1980 it resumed its regular oscillatory regime at full amplitude (Fernie 1981). HD 161796, on the other hand is the only Cepheid in which mode-switching has definitely been observed (cf.

O" ••••••: " , . " -. 0.. 0_004 ..... 002 Fig. - Oscillation properties of the ZZ Ceti star GD 226-29; (a) relative brightness variation over a time-stretch of 30 minutes, and (b) corresponding power spectrum (Kepler et al 1983). ,. 7 00 1. '-. '''~/ '#.. 730 800 U T 900 8~ 930 1000 TIME {28 MAY 19821 -4L------oo~I----~O~~~--~OO~3~--~O~04~--~OO~5~--~OO~6~--~OO~7~--~O~08~--~ F'REOUENCY (Hz) Fig. - The pulsation of the DB white dwarf GD 358; (a) brightness variation, and (b) power spectrum (Winget et al 1982).

1), with local periods of 80 to 1000 d, were recorded since 1596. Figs. 9 display the light curves of two well studied Mira stars. Fig. 9a. is a recent compilation of the visual brightness of R Aquilae by Davis (1982), while Fig. 9b. is an old record of the light curve of X Cygni extending over a period of almost a hundred years (Merrill 1938). The latter star's variability was discovered by Kirch in 1687; the variability of R Agl was discovered by Argelander in 1856 (cf Hagen 1921 for historical details).

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