PreprintCC BY 4.0arXiv
Foliations forcing closed orbits
Abstract
We study foliations which force every transverse flow to have a closed orbit. We fully characterize this property among C2 finite depth foliations on atoroidal 3-manifolds. We also show that for many foliations, this property can be broken by a C0-small modification of the foliation. We produce closed orbits using the theory of endperiodic maps, and we construct C1 flows without closed orbits by inserting dynamical plugs transverse to foliations along curves of attracting holonomy.
Related
- Stability of closed leaves holomorphic foliations via torsion behavior of groups of germs
- Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions
- CMC foliations on Euclidean spaces are minimal foliations
- ACC for lc thresholds for algebraically integrable foliations
- Transversely projectively flat foliations
BibTeX
@misc{buckminster2026foliations,
title = {{Foliations forcing closed orbits}},
author = {Ellis Buckminster and Audrey Rosevear},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10558},
eprint = {2610.10558},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10558},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Foliations forcing closed orbits
AU - Ellis Buckminster
AU - Audrey Rosevear
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.10558
UR - https://arxiv.org/abs/2610.10558
AB - We study foliations which force every transverse flow to have a closed orbit. We fully characterize this property among C^2 finite depth foliations on atoroidal 3-manifolds. We also show that for many foliations, this property can be broken by a C^0-small modification of the foliation. We produce closed orbits using the theory of endperiodic maps, and we construct C^1 flows without closed orbits by inserting dynamical plugs transverse to foliations along curves of attracting holonomy.
ER -