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A suspension of the Hénon map by periodic orbits

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  • Starrett, John
  • Nicholas, Craig

Abstract

We create polynomial differential equations for a suspension of the Hénon map embedded in R3. By globalizing the local tangent vectors to suspended periodic orbits of the Hénon map, we are able to find approximate autonomous differential equations for that geometric suspension. Using as few as two suspended periodic orbits, we can generate a robust three dimensional attractor whose Poincaré map has very nearly the dynamics of the original Hénon map on the attractor.

Suggested Citation

  • Starrett, John & Nicholas, Craig, 2012. "A suspension of the Hénon map by periodic orbits," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1486-1493.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:12:p:1486-1493
    DOI: 10.1016/j.chaos.2012.07.013
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