Communications in Mathematical Physics

, Volume 225, Issue 2, pp 275-304

From Invariant Curves to Strange Attractors

  • Qiudong WangAffiliated withDept. of Math., University of Arizona, Tucson, AZ 85721, USA. E-mail: dwang@math.arizona.edu
  • , Lai-Sang Young YoungAffiliated withCourant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USA.¶E-mail: lsy@cims.nyu.edu

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Abstract:

We prove that simple mechanical systems, when subjected to external periodic forcing, can exhibit a surprisingly rich array of dynamical behaviors as parameters are varied. In particular, the existence of global strange attractors with fully stochastic properties is proved for a class of second order ODEs.