This book is an edited version of lectures given by the authors at the 1985 Jilin University Summer School on Laser Physics. The School was held at Jilin University in Changchun, Peoples' Republic of China.

This volume contains the lectures and seminars presented at the NATO Advanced Study Institute on "Physics of New Laser Sources," the twelfth course of the Europhysics School of Quantum Electronics, held under the supervision of the Quantum Electronics Division of the European Physical Society. The Institute was held at Centro "I Cappuccini" San Miniato, Tuscany, July 11-21, 1984. The Europhysics School of Quantum Electronics was started in 1970 with the aim of providing instruction for young researchers and advanced students already engaged in the area of quantum electronics or for those wishing to switch into this area after working previously in other areas. From the outset, the School has been under the direction of Prof. F. T. Arecchi, then at the University of Pavia, now at the University of Florence, and Dr. D. Roess of Heraeus, Hanau. In 1981, Prof. H. Walther, University of Munich and Max-Planck Institut fur Quantenoptik joined as co-director. Each year the Directors choose a subj ct of particular interest, alternating fundamental topics with technological ones, and ask colleagues specifically competent in the chosen areas to take the scientific responsibility for that course.

This volume serves as a general introduction to the state of the art of quantitatively characterizing chaotic and turbulent behavior. It is the outgrowth of an international workshop on "Quantitative Measures of Dynamical Complexity and Chaos" held at Bryn Mawr College, June 22-24, 1989. The workshop was co-sponsored by the Naval Air Development Center in Warminster, PA and by the NATO Scientific Affairs Programme through its special program on Chaos and Complexity. Meetings on this subject have occurred regularly since the NATO workshop held in June 1983 at Haverford College only two kilometers distant from the site of this latest in the series. At that first meeting, organized by J. Gollub and H. Swinney, quantitative tests for nonlinear dynamics and chaotic behavior were debated and promoted [1). In the six years since, the methods for dimension, entropy and Lyapunov exponent calculations have been applied in many disciplines and the procedures have been refined. Since then it has been necessary to demonstrate quantitatively that a signal is chaotic rather than it being acceptable to observe that "it looks chaotic". Other related meetings have included the Pecos River Ranch meeting in September 1985 of G. Mayer Kress [2) and the reflective and forward looking gathering near Jerusalem organized by M. Shapiro and I. Procaccia in December 1986 [3). This meeting was proof that interest in measuring chaotic and turbulent signals is widespread.

This book is an edited version of lectures given by the authors at the 1985 Jilin University Summer School on Laser Physics. The School was held at Jilin University in Changchun, Peoples' Republic of China.