A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I

@article{Kaloshin2000ASE,
title={A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I},
author={Vadim Kaloshin and Brian R. Hunt},
journal={Electronic Research Announcements of The American Mathematical Society},
year={2000},
volume={7},
pages={17-27}
}
• Published 21 December 2000
• Mathematics
• Electronic Research Announcements of The American Mathematical Society
For diffeomorphisms of smooth compact manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for C2 or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we…
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