PreprintarXiv licencearXiv
On the Hausdorff dimension of oscillatory motions in three-body problems
Abstract
We show that for the Sitnikov example and for the restricted planar circular 3-body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains for both problems.
Related
- Inverse Heat Source Problems from Boundary Flux and Interior Observations on Sets of Low Hausdorff Dimension
- Foliated Plateau problems, surface Radon transforms, and boundary area rigidity in dimension three
- Holomorphic motions, Assouad dimension and quasiconformal mappings
- Valeur exacte de la mesure de Hausdorff d'un sous-ensemble fractal de dimension log 3 / log 4 du triangle de Sierpinski
- Effective Hausdorff dimension one is cofinal in the K-degrees
BibTeX
@misc{gorodetski2026hausdorff,
title = {{On the Hausdorff dimension of oscillatory motions in three-body problems}},
author = {Anton Gorodetski and Vadim Kaloshin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25750},
eprint = {2610.25750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25750},
}
RIS
TY - UNPB
TI - On the Hausdorff dimension of oscillatory motions in three-body problems
AU - Anton Gorodetski
AU - Vadim Kaloshin
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25750
UR - https://arxiv.org/abs/2610.25750
AB - We show that for the Sitnikov example and for the restricted planar circular 3-body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains for both problems.
ER -