# On the ergodic properties of nowhere dispersing billiards

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### Cites background from "On the ergodic properties of nowher..."

...However, by excluding from the billiard a spherical region inside the polyhedron, one can make the dynamics hyperbolic [Bunimovich, 1979]....

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### "On the ergodic properties of nowher..." refers background in this paper

...For example, it is known [ 20 ] that the billiard in ellips is a completely integrable system....

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### "On the ergodic properties of nowher..." refers background in this paper

...The following three lemmas can be easily proved with the help of elementary geometrical considerations, the corresponding proofs can be found for instance in [1] (see also [2], where some corrections and specifications are given)....

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...One can work out the following stages of the demonstration of the K-property for our billiards, in analogy with paper [5] (see also [1,2]), with some minor modifications, β-property can be concluded from K-property just in the same way as for dispersing billiards (see [17])....

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...for almost every point xeύl/v The process of construction of these fibers is a variant of the proof of HadamarPerron's theorem for manifolds (see [1, 14])....

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...In complete analogy with the case of dispersing billiards (see [1], pp....

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...(The proof of convergence of κ\x) for dispersing billiards is trivial [1,2]....

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### "On the ergodic properties of nowher..." refers background in this paper

...Such fibers play a central role in studying of ergodic properties of classical dynamical systems, such as Anosov systems, partially hyperbolic systems, dispersing billiards and so on (see [14-16])....

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349 citations