From Limit Cycles to Strange Attractors
Abstract
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 preciselydefined dynamical properties that together imply chaos that is both sustained in time and physically observable.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 May 2010
 DOI:
 10.1007/s002200100994y
 arXiv:
 arXiv:1004.0019
 Bibcode:
 2010CMaPh.296..215O
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 37D25;
 37D45
 EPrint:
 27 pages