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Titlebook: Ergodic Concepts in Stellar Dynamics; Proceedings of an In V. G. Gurzadyan,D. Pfenniger Conference proceedings 1994 Springer-Verlag Berlin

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978-3-662-13986-8Springer-Verlag Berlin Heidelberg 1994
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Ergodic Concepts in Stellar Dynamics978-3-540-48386-1Series ISSN 0075-8450 Series E-ISSN 1616-6361
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https://doi.org/10.1007/978-3-663-07143-3The properties of the billiard vary with the energy E of the bouncing ball. These are explored through the surface of section. The billiard is almost integrable for very small or very large values of E. It looks ergodic in a range of values of E. The main families of periodic orbits are shown.
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On a notion of weak stability and its relevance for celestial mechanics and molecular dynamics,The stability problem in Hamiltonian dynamics is discussed in the light of Nekhoroshev‘s theorem. This guarantees a form of weak stability, namely referred to finite (rather than infinite) times. Applications are discussed for the restricted problem of three bodies and for the problem of energy equipartition in statistical mechanics.
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