It seems very strange that quadratic maps pass from regular to chaotic
dynamics by infinitesimal change of c value. But
strange Cantor repeller results in chaotic transient
orbits (with positive Lyapunov exponent L > 0).
These orbits appear for c values corresponding to regular dynamics
windows. For large n these orbits go to attracting cycle. Chaotic
transient length depends strongly on starting point xo .
c = -1.5749 corresponds to the superstable period-7 cycle.
Chaotic transient length grows for more narrow windows of regular dynamics.
Therefore for tiny windows (near any chaotic c value) one can
distinguish regular or chaotic dynamics only for very long iterations.
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updated 8 Nov 2006