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Standard maps on the torus
Map Move with the mouse over the parameter values. The pictures were generated with Mathematica 3.0 under Linux .
Chirikov 0-Energy Anosov-Arnold Wojtkowski S-B-K-P
(x,y) -> (2x-y + g sin(x),x). (x,y) -> (-y + g sin(x),x). (x,y) -> (4x-y + g sin(x),x) Anosov for |g|<2. (x,y) -> (2x-y + g f(x),x) piecewise linear f. (x,y)->(2x-y+ 4 arg(1+g exp(-ix)),x). integrable
Standard g=0.5 Zero Energy g=0.5 Anosov-Arnold g=1.7 Wojtkowski g=0.5 Bobenko g=0.0
Standard g=0.9 Zero Energy g=0.9 Anosov-Arnold g=2.1 Wojtkowski g=0.9 Bobenko g=0.2
Standard g=1.3 Zero Energy g=1.3 Anosov-Arnold g=2.5 Wojtkowski g=1.3 Bobenko g=0.4
Standard g=1.7 Zero Energy g=1.7 Anosov-Arnold g=2.9 Wojtkowski g=1.7 Bobenko g=0.6
Standard g=2.1 Zero Energy g=2.1 Anosov-Arnold g=3.3 Wojtkowski g=2.1 Bobenko g=0.8
Standard g=2.5 Zero Energy g=2.5 Anosov-Arnold g=3.7 Wojtkowski g=2.5 Bobenko g=1.0
Maps in the plane