article
Generic diffeomorphisms with superexponential growth of number of periodic orbits
published
yes
Vadim
Kaloshin
author FE553552-CDE8-11E9-B324-C0EBE56974250000-0002-6051-2628
Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.
Springer Nature2000
eng
Mathematical PhysicsStatistical and Nonlinear Physics
Communications in Mathematical Physics
0010-3616
1432-091610.1007/s002200050811
211253-271
yes
Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2000. <a href="https://doi.org/10.1007/s002200050811">https://doi.org/10.1007/s002200050811</a>.
Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. 2000;211:253-271. doi:<a href="https://doi.org/10.1007/s002200050811">10.1007/s002200050811</a>
V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.
Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>, vol. 211, Springer Nature, 2000, pp. 253–71, doi:<a href="https://doi.org/10.1007/s002200050811">10.1007/s002200050811</a>.
Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s002200050811">https://doi.org/10.1007/s002200050811</a>
Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.
V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” <i>Communications in Mathematical Physics</i>, vol. 211. Springer Nature, pp. 253–271, 2000.
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