Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.15611 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929642345070592 |
|---|---|
| author | Kochetkov, Yury Pyatko, Lev |
| author_facet | Kochetkov, Yury Pyatko, Lev |
| contents | In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be not more, than three of them). We formulate conjectures and prove some statements. For example, if a pyramid has two orthogonal faces, then it has not more than two 4-cycles. Also we study 4-cycles of the "physical" billiard in pyramids, i.e. in the presence of gravity. Here we present our observations for a generic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematical and physical billiard in pyramids Kochetkov, Yury Pyatko, Lev Dynamical Systems Metric Geometry In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be not more, than three of them). We formulate conjectures and prove some statements. For example, if a pyramid has two orthogonal faces, then it has not more than two 4-cycles. Also we study 4-cycles of the "physical" billiard in pyramids, i.e. in the presence of gravity. Here we present our observations for a generic case. |
| title | Mathematical and physical billiard in pyramids |
| topic | Dynamical Systems Metric Geometry |
| url | https://arxiv.org/abs/2412.15611 |