The size of the shadow boundary pojection.
Velocity and Entropy of Motion in Periodic Potentials
This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti. We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities. The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.
The -centre problem of celestial mechanics for large energies
We consider the classical three-dimensional motion in a potential which is the sum of attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the centres, we find a universal behaviour for all energies above a positive threshold. Whereas for there are no bounded orbits, and for there is just one closed orbit, for the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....
The phase transition of the number-theoretical spin chain.
Maximizing multi–information
Stochastic interdependence of a probability distribution on a product space is measured by its Kullback–Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed description of the structure of probability distributions with globally maximal multi-information we obtain our main result: The exponential family...
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