 9953 Sza'sz D.
 BallAvoiding Theorems
(98K, amstex)
Feb 16, 99

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Abstract. Consider a nice hyperbolic dynamical system (singularities not excluded).
Statements about the topological smallness of the subset of orbits,
which avoid an open subset of the phase space  for every moment of time,
or just for a not too small subset of times  play a key role in showing
hyperbolicity or ergodicity of semidispersive billiards, in particular, of
hard ball systems. Beside surveying the characteristic results, called
ballavoiding theorems, and giving an idea of the methods of their proofs,
their applications are also illustrated. Further we also discuss analogous
questions (which had arisen, for intance, in number theory), when Hausdorff
dimension is taken instead of the topological one. The answers strongly
depend on the notion of dimension which is used. Finally, ball avoiding
subsets are naturally related to repellers extensively studied by
physicists. For the interested reader we also sketch some analytic and
rigorous results about repellers and escape times.
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