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The modifications that quantum mechanics imposes on the general picture of classical chaos is a subject of growing interest for its theoretical relevance and for different physical applications as well. As a matter of fact the study of nonlinear dynamical systems has led to a much better understanding of the rich complexity of the classical motion. Of particular relevance was the discovery of the deterministic chaotic motion which is a type of motion indistinguishable from a purely random motion even if it is governed by strictly deterministic laws. This motion is charac- terized by exponential instability of orbits with respect to initial conditions which leads to exponential loss of memory, decay of correlations and approach to statistical equilibrium. more...

Scaling Function Dynamics M.J. Feigenbaum. Renormalization, Zygmund Smoothness and the Epstein Class D. Sullivan. Torus Maps R.S. MacKay. Quasiperiodicity, ModeLocking, and Universal Scaling in Rayleigh-Benard Convection R.E. Ecke. Patterns in Chaos B.V. Chirikov. Spatiotemporal Chaos J.P. Eckmann, et al. Topics in Pattern Formation Problems and Related Questions Y. Pomeau. Growth Patterns: From Stable Curved Fronts to Fractal Structures Y. Couder. Simple and Complex Patterns in Coupled Map Lattices L. Bunimovich. State Space Reconstruction and Noise M. Casdagli, et al. Global Implications of the Implicit Function Theorem K.A. Alligood, et al. Unfolding Complexity and Modeling Asymptotic Scaling Behavior R. Badii, et al. Index. more...

We discuss the quantum behaviour of systems which exhibit deterministic chaos in the classical limit. To this end we first examine the motion of a rotator under an external time-periodic δ-like perturbation. When the perturbation is strong enough, the classical motion is chaotic and diffusive while the quantum excitation remains strongly localized. A similar phenomenon takes place in the more physical problem of an hydrogen atom irradiated by a linearly polarized microwave field. In this latter case however, there exists a critical value of the microwave field intensity above which localization is destroyed and strong quantum excitation takes place. Numerical computations confirm the above theoretical predictions which also agree with the experimental results so far available. more...

A whole session in this Conference has been devoted to fluctuations in Nuclear Spectra and related topics. In the organizers’ mind, this fact was meant as an acknowledgment of the close relationship existing between two originally very different problems. more...

Our understanding of the qualitative features of classical systems has greatly improved after the discovery of the so called deterministic chaotic motion. This type of motion is characterized by exponential instability of almost all orbits with respect to initial conditions. In turns this instability leads to loss of memory of initial conditions, decay of correlations and approach to statistical equilibrium. more...