2013 · 25 citations · 18 references
Natural SciencesMathematicsPhysicsComplex SystemsDynamical SystemsStochastic ProcessesBifurcation TheoryChaos TheoryErgodic TheoryFixed PointsLimit CyclesNonlinear DynamicsAttractor DynamicsAttractorsChaotic DynamicsLimit Cycle DynamicsStrange Attractors
Abstract. We define a quantitative notion of shear for limit cycles of flows. We prove that strange attrac-tors 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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Michael Benedicks, Lennart Carleson · Annals of Mathematics · 1991 · 706 citations
Recurrence times and rates of mixing
Lai‐Sang Young · Israel Journal of Mathematics · 1999 · 682 citations