53 citations · 284 across the 40 of their papers we have counts for
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math.DS1999
An extension of the Artin-Mazur theorem
Vadim Yu. Kaloshin
Let M be a compact manifold. We call a mapping f in C^r(M,M) an Artin-Mazur mapping if the number of isolated periodic points of f^n grows at most exponentially in n. Artin and Maz…
math.DS1999★ 50 cited
Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits
Vadim Kaloshin
Consider a compact manifold M of dimension at least 2 and the space of C^r-smooth diffeomorphisms Diff^r(M). The classical Artin-Mazur theorem says that for a dense subset D of Dif…