Asian Journal of Mathematics
Volume 25 (2021)
Finsler perturbation with nondense geodesics with irrational directions
Pages: 715 – 726
We show that given any Liouville direction and flat Finsler torus, one can make a $C^\infty$‑small perturbation on an arbitrarily small disc to get a nondense geodesic in the given direction.
Finsler geometry, perturbation, nondense geodesics, dual lens maps, Aubry–Mather theory
2010 Mathematics Subject Classification
The first-named author was partially supported by NSF grant DMS-1205597.
The second-named author was partially supported by NSF grant DMS-1205597 and D. Burago’s PSU Research Fund.
Received 18 February 2019
Accepted 17 June 2021
Published 6 July 2022