Symplectic reversible maps, tiles and chaos

✍ Scribed by Igor Hoveijn

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 494 KB
• Volume: 2
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/0960-0779(92)90049-s

✦ Synopsis

The symplectic map F(z) = R,~z + ef(x)(-sin o:, cos ol), where R~ is a rotation, produces a periodic tiling of the phase-plane for some values of a ~ if f is a periodic function. Due to the periodicity of the map, the chaotic regions of the hyperbolic fixed points of the appropriate iterate of F are connected, thereby allowing large scale diffusion in a two dimensional map. In the non periodic case large scale diffusion does not seem possible for all values of e. An approximating integrable system is constructed. We also consider the effect of nonsymplectic perturbations. *Communicated by F. Verhulst.

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