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.
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.
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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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