FAMILY OF INVARIANT CANTOR SETS AS ORBITS OF DIFFERENTIAL EQUATIONS

The invariant Cantor sets of the logistic map gµ(x) = µx(1 − x) for µ> 4 are hyperbolic and form a continuous family. We show that this family can be obtained explicitly through solutions of infinitely coupled differential equations due to the hyperbolicity. The same result also applies to the tent map Ta(x) = a(1/2 − |1/2 − x|) for a> 2