[Classification complète des cycles homoclines de dans le cas d'un groupe de symétrie ]
Des cycles homoclines avec groupes de symétrie contenus dans SO(4) sont déjà apparus dans la littérature. Ces cycles ont 2, 3, 6, 8, 12 ou 24 points d'équilibre. Dans cette Note, on montre que cette classification est complète en utilisant un résultat sur les équations diophantiennes à angles rationnels.
Some homoclinic cycles in with symmetry groups contained in SO(4) have already appeared in the literature. These cycles have 2, 3, 6, 8, 12, or 24 equilibria. In this Note we show that this classification is complete using a result in diophantine trigonometric equations with rational angles.
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Nicola Sottocornola 1
@article{CRMATH_2002__334_10_859_0, author = {Nicola Sottocornola}, title = {Complete classification of homoclinic cycles in $ \mathbb{R}^{\mathbf{4}}$ in the case of a symmetry group $ \mathbf{G\subset }\mathrm{SO}\mathbf{(4)}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {859--864}, publisher = {Elsevier}, volume = {334}, number = {10}, year = {2002}, doi = {10.1016/S1631-073X(02)02371-3}, language = {en}, }
TY - JOUR AU - Nicola Sottocornola TI - Complete classification of homoclinic cycles in $ \mathbb{R}^{\mathbf{4}}$ in the case of a symmetry group $ \mathbf{G\subset }\mathrm{SO}\mathbf{(4)}$ JO - Comptes Rendus. Mathématique PY - 2002 SP - 859 EP - 864 VL - 334 IS - 10 PB - Elsevier DO - 10.1016/S1631-073X(02)02371-3 LA - en ID - CRMATH_2002__334_10_859_0 ER -
%0 Journal Article %A Nicola Sottocornola %T Complete classification of homoclinic cycles in $ \mathbb{R}^{\mathbf{4}}$ in the case of a symmetry group $ \mathbf{G\subset }\mathrm{SO}\mathbf{(4)}$ %J Comptes Rendus. Mathématique %D 2002 %P 859-864 %V 334 %N 10 %I Elsevier %R 10.1016/S1631-073X(02)02371-3 %G en %F CRMATH_2002__334_10_859_0
Nicola Sottocornola. Complete classification of homoclinic cycles in $ \mathbb{R}^{\mathbf{4}}$ in the case of a symmetry group $ \mathbf{G\subset }\mathrm{SO}\mathbf{(4)}$. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 859-864. doi : 10.1016/S1631-073X(02)02371-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02371-3/
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