Generic diffeomorphisms with superexponential growth of number of periodic orbits
Kaloshin, Vadim
Mathematical Physics
Statistical and Nonlinear Physics
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 Nature
2000
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/8525
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>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/s002200050811
info:eu-repo/semantics/altIdentifier/issn/0010-3616
info:eu-repo/semantics/altIdentifier/issn/1432-0916
info:eu-repo/semantics/closedAccess