A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I
V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 17–27.

A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 28–36.