Cantori, islands and asymptotic curves in the stickiness region
The paper gives a numerical study of the dynamics on a 2D-torus generated by the following model map: \[ \begin{aligned} & x_{i+1}:=x_i+y_{i+1}\pmod 1\\ & y_{i+1}:=y_i+\frac K{2\pi}\sin(2\pi x_i)\pmod 1 \end{aligned} \] where \(K\) is an appropriate nonlinearity parameter. The resonant structure near a noble cantorus and the islands of stability located near the gaps of the cantorus are investigated. The crossing of the gaps of the cantorus by the asymptotic curves of unstable periodic orbits is also numerically verified. Moreover, the influence of these structures on the phenomena of stickiness is discussed.
scientific article; zbMATH DE number 1442264