We construct a 3-dimensional billiard realizing all links as collections of isotopy classes of periodic orbits. For every branched surface supporting a semi-flow, we construct a 3d-billiard whose collections of periodic orbits contain those of the branched surface. R. Ghrist constructed a knot-holder containing any link as collection of periodic orbits. Applying our construction to his example provides the desired billiard.
On construit un billard tridimensionnel réalisant tout entrelacs fini comme collection dʼorbites périodiques. Plus généralement, étant donné un patron, cʼest-à-dire une surface branchée munie dʼun semi-flot, on construit un billard dont la collection des orbites périodiques contient celle du patron. R. Ghrist a construit un tel patron contenant tous les entrelacs. On obtient le billard souhaité en appliquant notre construction à son exemple.
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Pierre Dehornoy 1
@article{CRMATH_2011__349_9-10_575_0, author = {Pierre Dehornoy}, title = {A billiard containing all links}, journal = {Comptes Rendus. Math\'ematique}, pages = {575--578}, publisher = {Elsevier}, volume = {349}, number = {9-10}, year = {2011}, doi = {10.1016/j.crma.2011.04.003}, language = {en}, }
Pierre Dehornoy. A billiard containing all links. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 575-578. doi : 10.1016/j.crma.2011.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.003/
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