Figure 9

The present figure explains the twist effect due to the different periods of${\mathbf{\Gamma }}^{{\mathit{\ell }}_{\mathbf{1}}}$and${\mathbf{\Gamma }}^{{\mathit{\ell }}^{\mathbf{\ast }}}$. We have considered the evolution of the part of ℒ with $x\ge 0$ connecting $P_{+}$ to the point R for two different time gaps: $t_{+}-t_{-}=5.5$ and $t_{+}-t_{-}=50$. The corresponding two images $\mathrm{\Phi }(P_{+})$ are indicated by a cross, while the images $\mathrm{\Phi }(R)$ are marked by a black dot. The parameters used are $k=1$, ${\mu }_1=2$, ${\mu }_0=1/2$, as before. Notice that the two images $\mathrm{\Phi }(P_{+})$, although close to each other in the figure, have made a different number of turns around the origin. For graphical reasons, a slightly different x- and y-scaling has been used.