This is an extended report on a problem session about geodesic flows held on May 30, 1984 at MSRI , Berkeley. The list of six authors reflects the principal participants in the discussion. Contributions of other participants are mentioned in the text. The session was chaired by A. Katok; this report was prepared by K. Burns in collaboration with A. Katok.
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Burns et al. (1985) studied this question.
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