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

UR - http://www.scopus.com/inward/record.url?scp=75149119641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75149119641&partnerID=8YFLogxK

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 -