Edward A. Spiegel – författare

The per iod of an oscillator tells us much about its structure. J. J. Thomson's deduction that a particle with the e/rn of an electron was in the atom is perhaps the most stunning instance. For us, the deduction of the mean density of a star from its oscillation period is another important example. What then can we deduce about an oscillator that is not periodic? If there are several frequencies or if the behavior is chaotic, may we not hope to learn even more delicate vital statistics about its workings? The recent progress in the theory of dynamical systems, particularly in the elucidat ion of the nature of chaos, makes it seem reasonable to ask this now. This is an account of some of the happenings of a workshop at which this question was raised and discussed. ~iTe were inc0rested in seeing ways in which the present understanding of chaos might guide astrophysical modelling and the interpretation of observations. But we did not try to conceal that we were also interested in chaos itself, and that made for a pleasant rapport between the chaoticists and astrophysicists at the meeting. We have several introductory papers on chaos in these proceedings, particularly on the analysis of data from systems that may be suspected of chaotic behavior. The papers of Geisel, Grassberger and Guckenheimer introduce the ways of characterizing chaos and Perdang illustrates how some of these ideas may be put into practice in explicit cases.

In January 1937, Nobel laureate in Physics Subrahmanyan Chandrasekhar was recruited to the University of Chicago. He was to remain there for his entire career, becoming Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics in 1952 and attaining emeritus status in 1985. This is where his then student Ed Spiegel met him during the summer of 1954, attended his lectures on turbulence and jotted down the notes in hand. His lectures had a twofold purpose: they not only provided a very elementary introduction to some aspects of the subject for novices, they also allowed Chandra to organize his thoughts in preparation to formulating his attack on the statistical problem of homogeneous turbulence. After each lecture Ed Spiegel transcribed the notes and filled in the details of the derivations that Chandrasekhar had not included, trying to preserve the spirit of his presentation and even adding some of his side remarks. The lectures were rather impromptu and the notes as presented here are as they were set down originally in 1954. Now they are being made generally available for Chandrasekhar’s centennial.

In January 1937, Nobel laureate in Physics Subrahmanyan Chandrasekhar was recruited to the University of Chicago. He was to remain there for his entire career, becoming Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics in 1952 and attaining emeritus status in 1985. This is where his then student Ed Spiegel met him during the summer of 1954, attended his lectures on turbulence and jotted down the notes in hand. His lectures had a twofold purpose: they not only provided a very elementary introduction to some aspects of the subject for novices, they also allowed Chandra to organize his thoughts in preparation to formulating his attack on the statistical problem of homogeneous turbulence. After each lecture Ed Spiegel transcribed the notes and filled in the details of the derivations that Chandrasekhar had not included, trying to preserve the spirit of his presentation and even adding some of his side remarks. The lectures were rather impromptu and the notes as presented here are as they were set down originally in 1954. Now they are being made generally available for Chandrasekhar’s centennial.

The per iod of an oscillator tells us much about its structure. J. J. Thomson''s deduction that a particle with the e/rn of an electron was in the atom is perhaps the most stunning instance. For us, the deduction of the mean density of a star from its oscillation period is another important example. What then can we deduce about an oscillator that is not periodic? If there are several frequencies or if the behavior is chaotic, may we not hope to learn even more delicate vital statistics about its workings? The recent progress in the theory of dynamical systems, particularly in the elucidat ion of the nature of chaos, makes it seem reasonable to ask this now. This is an account of some of the happenings of a workshop at which this question was raised and discussed. ~iTe were inc0rested in seeing ways in which the present understanding of chaos might guide astrophysical modelling and the interpretation of observations. But we did not try to conceal that we were also interested in chaos itself, and that made for a pleasant rapport between the chaoticists and astrophysicists at the meeting. We have several introductory papers on chaos in these proceedings, particularly on the analysis of data from systems that may be suspected of chaotic behavior. The papers of Geisel, Grassberger and Guckenheimer introduce the ways of characterizing chaos and Perdang illustrates how some of these ideas may be put into practice in explicit cases.