From Limit Cycles to Strange Attractors

  title={From Limit Cycles to Strange Attractors},
  author={William Ott and Mikko Stenlund},
  journal={Communications in Mathematical Physics},
  • W. Ott, Mikko Stenlund
  • Published 31 March 2010
  • Mathematics, Physics
  • Communications in Mathematical Physics
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable. 
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  • G. Gottwald, I. Melbourne
  • Mathematics, Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2004
We describe a new test for determining whether a given deterministic dynamical system is chaotic or non–chaotic. In contrast to the usual method of computing the maximal Lyapunov exponent, our method