TY - JOUR
T1 - Tangent bundle viewpoint of the Lorenz system and its chaotic behavior
AU - Yajima, Takahiro
AU - Nagahama, Hiroyuki
N1 - Funding Information:
The authors are sincerely grateful to Prof. T. Aikou for his helpful and valuable comments. One of the authors (T. Yajima) was financially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists , the Global COE (Centers of Excellence) Program: “Global Education and Research Center for Earth and Planetary Dynamics” of Tohoku University and Research Assistant Fellowship of Graduate School of Science of Tohoku University .
PY - 2010/3/1
Y1 - 2010/3/1
N2 - 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).
AB - 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).
KW - Chaos
KW - Euler-Poincaré equation
KW - Geometrical invariants
KW - Lie-Poisson equation
KW - Lorenz system
KW - Tangent bundle
KW - Torsion
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U2 - 10.1016/j.physleta.2010.01.025
DO - 10.1016/j.physleta.2010.01.025
M3 - Article
AN - SCOPUS:75149119641
SN - 0375-9601
VL - 374
SP - 1315
EP - 1319
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 11-12
ER -