TY - JOUR
T1 - Generic Equidistribution of Periodic Orbits for Area-Preserving Surface Maps
AU - Prasad, Rohil
N1 - Publisher Copyright:
© 2022 The Author(s) 2023.
PY - 2024/12/1
Y1 - 2024/12/1
N2 - We prove that a C∞-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem for area-preserving surface diffeomorphisms. The proof has two ingredients. The first is a "Weyl law"for PFH spectral invariants, which was used to prove the generic density theorem. The second is a variational argument inspired by the work of Marques-Neves-Song and Irie on equidistribution results for minimal hypersurfaces and three-dimensional Reeb flows, respectively.
AB - We prove that a C∞-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem for area-preserving surface diffeomorphisms. The proof has two ingredients. The first is a "Weyl law"for PFH spectral invariants, which was used to prove the generic density theorem. The second is a variational argument inspired by the work of Marques-Neves-Song and Irie on equidistribution results for minimal hypersurfaces and three-dimensional Reeb flows, respectively.
UR - https://www.scopus.com/pages/publications/85183535438
UR - https://www.scopus.com/inward/citedby.url?scp=85183535438&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnac340
DO - 10.1093/imrn/rnac340
M3 - Article
AN - SCOPUS:85183535438
SN - 1073-7928
VL - 2024
SP - 14802
EP - 14834
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 24
ER -