Chaotic Attractors of Relaxation Oscillators

@inproceedings{Guckenheimer2006ChaoticAO,
  title={Chaotic Attractors of Relaxation Oscillators},
  author={John Guckenheimer and Martin Wechselberger and Lai-Sang Young},
  year={2006}
}
We develop a general technique for proving the existence of chaotic attractors for three dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of… CONTINUE READING
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