96-352 Knill O.

Four papers in dynamics. (125K, four LaTeX files (to unbundle, sh the downloaded file)) Aug 6, 96

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Abstract. 1. ON THE DYNAMICS OF A GENERAL UNITARY OPERATOR: The topological dynamical system obtained by a unitary operator acting on the unit ball of a Hilbert space has zero topological entropy. 2. SINGULAR CONTINUOUS SPECTRUM AND QUANTITATIVE RATES OF WEAKLY MIXING: Singular continuous spectrum is generic in ergodic theory. Quantitative weak mixing properties are related to spectral properties of the spectral measures. 3. A REMARK ON QUANTUM DYNAMICS: A discrete-time Schr\"odinger evolution is useful for getting information on spectral measures of Schr\"odinger operators. 4. NONLINEAR DYNAMICS FROM THE WILSON LAGRANGIAN: Critical points of a functional related to the Wilson action define a nonlinear discrete equation. The evolution is in the simplest case a cubic Henon map and more generally a Hamiltonian coupled map lattice.

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