Communications in Mathematical Physics

, Volume 296, Issue 1, pp 215–249 | Cite as

From Limit Cycles to Strange Attractors



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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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA
  3. 3.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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