Gauss lemniscate functions as exact solutions for chaotic maps
A.F. Golubentsev, V.M. Anikin
Department of Physics, Saratov State University, Saratov, Russia
The chaotic transformation:
is characterized by invariant measure:
Lyapunov number ln 2 and exact solution:
where sl(u) is Gauss lemniscate sinus, c=2.622... The chaotic map:
is decribed by invariant measure:
Lyapunov number ln 2 and exact solution:
where cl(u) is Gauss lemniscate cosinus.