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Titlebook: Nonlinear Evolution and Chaotic Phenomena; Giovanni Gallavotti,Paul F. Zweifel Book 1988 Plenum Press, New York 1988 Renormalization group

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Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Care records the fine scale geometrical structure. We will discuss two examples from the theory of one dimensional smooth dynamical systems, namely Cantor sets dynamically defined by i) folding maps on the boundary of chaos,and by ii) smooth expanding maps.
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Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Pertuditions of metaequilibrium rather than in conditions of equilibrium, an show how a mathematical support to such point of view is given by the recent Nekhoroshev theorem of perturbation theory. As an application, we report the deduction of Planck’s law in a classical context already given by Nernst,
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Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions time scales rigorously introduced by recent results of classical perturbation theory. The possible relevance for the problem of comparing theoretical previsions with experimental results in statistical models is pointed out.
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A Simple and Compact Presentation of Birkhoff Seriestors yields a compact expression, which actually is a formal summation of the recurrence formulas usually obtained for the normal form of a quasi-integrable hamiltonian..Talk given at the school: “Non Linear Evolution and Chaotic Phenomena”-Noto, June 87
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Two Lectures on Chaotic Dynamics in the Solar Systemsolar system are published in Wisdom (1987) .. ., 109 and in somewhat greater detail in Wisdom (1987) . ., in press. Only an abstract of the topics will be given here, with references to the original literature. References to associated literature may be found in the cited references
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Quantum Chaology of Energy Levels Notes Based on Lectures by Michael Berrya system are known to depend critically on the form of the Hamiltonian and the phase space may support regions of regular and chaotic motion interwoven on all scales.. A natural question is: how does this classical complexity manifest itself in the corresponding quantum system? Sometimes this questi
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