Multiplicity of closed geodesics on odd-dimensional bumpy Finsler compact space form

@misc{liu2026multiplicity,
  title = {{Multiplicity of closed geodesics on odd-dimensional bumpy Finsler compact space form}},
  author = {Hui Liu and Linxinzi Qi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27685},
  eprint = {2610.27685},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27685},
}

TY  - UNPB
TI  - Multiplicity of closed geodesics on odd-dimensional bumpy Finsler compact space form
AU  - Hui Liu
AU  - Linxinzi Qi
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27685
UR  - https://arxiv.org/abs/2610.27685
AB  - Let M = S^2n+1/Γ be a manifold diffeomorphic to a compact space form, endowed with a bumpy Finsler metric F. In this paper, we prove that there exist at least n+3 contractible minimal closed geodesics on M, assuming that all contractible minimal closed geodesics have non-zero Morse indices. Here, a contractible closed geodesic is called minimal if it is not an iteration of any other contractible closed geodesic. In particular, this confirms the generalized Anosov-Katok conjecture for the bumpy quotient manifold (S^3/Γ, F) under the non-zero Morse index assumption.
ER  -