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トポロジー火曜セミナー
過去の記録 ～09/19｜次回の予定｜今後の予定 09/20～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2014年01月21日(火)
17:30-18:30 数理科学研究科棟(駒場) 056号室
李 暁龍 氏 (東京大学大学院数理科学研究科)
ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
李 暁龍 氏 (東京大学大学院数理科学研究科)
ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
[ 講演概要 ]
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.
