Torus Knot in a Dissipative Fifth-Order System.

• Bekki Naoaki

  Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA

抄録

In order to show that some periodic orbits of a fifth-order system of magnetoconvection are embedded in a three-dimensional subspace, main projections onto a three-dimensional subspace from the five-dimensional space are numerically investigated. It is found that the periodic orbits are topologically equivalent to a (p, q)-torus knot, where its curve closes after rotating q times in the meridional direction and p times in the longitudinal direction. In terms of a braid word for the torus knot, a (2, 7)-torus knot is finally obtained in the fifth-order system through the complicated bifurcations under parameter variation. This suggests that topological invariants embedded in a three-manifold can be extracted from realistic dissipative higher dimensional dynamical systems.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｐｈｙｓｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｐｈｙｓｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 69 (2), 295-298, 2000

  一般社団法人 日本物理学会

キーワード

• torus knot
• dissipative system
• magnetoconvection
• periodic orbit
• braid word
• topological invariant

詳細情報

• CRID: 1390282679158102016
• NII論文ID: 110001971351
• NII論文ID: 210000102513
• NII論文ID: 130004537411
• NII書誌ID: AA00704814
• DOI: 10.1143/jpsj.69.295
• BIBCODE: 2000JPSJ...69..295B
• ISSN: 13474073
• ISSN: 00319015
• MRID: 1769543
• NDL書誌ID: 5289887
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5289887
• Web Site: http://journals.jps.jp/doi/pdf/10.1143/JPSJ.69.295
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可