Tangent bundle viewpoint of the Lorenz system and its chaotic behavior

Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


A new geometric viewpoint of the Lorenz system is proposed based on a theory of tangent bundle. By introducing the geometrical viewpoints of second order system governed by Euler-Poincaré equation or Lie-Poisson equation, geometrical invariants of the Lorenz system can be obtained. Especially, a torsion tensor as one of geometrical invariants relates to the chaotic behavior characterized by the Rayleigh number, and results from the decomposition from the second order system to the tangent space (state space) and base space (configuration space).

Original languageEnglish
Pages (from-to)1315-1319
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number11-12
Publication statusPublished - 2010 Mar 1


  • Chaos
  • Euler-Poincaré equation
  • Geometrical invariants
  • Lie-Poisson equation
  • Lorenz system
  • Tangent bundle
  • Torsion


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