For a window with symbolic dynamics S we get its orbits as
composition of this pattern S and orbits of f_{c} .
E.g. composition of period-3 window pattern CLR and period-5 orbit CLRLL is period-15 orbit CLRRLRLLRRLRRLR . These two orbits make similar period-5 and period-15 windows on bifurcations diagrams above. It is evident, that f_{c}^{o3} map has the same CLRLL period-5 pattern (made of underlined letters) after interchanging L and R . |
"In a similar way" the band merging preperiodic point [CLR]L turns into [CLRRLRL]LRR one (but it is not very clear :) |
But these orbits are more complicated. Beyond the Feigenbaum point every "right" orbit is period doubling of corresponding "left" orbit, i.e. composition of the "left" orbit and period-2 orbit pattern CL . But below the Feigenbaum point we have reverse period doubling cascade, therefore every "right" orbit is composition of the pattern CL and the "left" orbit (see also Reverse period doubling cascades later).