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The Dimension of the Maximal Measure for a Polynomial Map

1984; Princeton University; Volume: 119; Issue: 2 Linguagem: Inglês

10.2307/2007044

1939-8980

Anthony Manning,

Functional Equations Stability Results

Let f: C -> C be a polynomial of degree d ? 2. The most interesting dynamics of f takes place on its Julia set J(f), an invariant compact perfect set which can be defined, for example, as the closure of the repelling periodic points. Brolin constructed the equilibrium distribution m on J(f), an ergodic measure which is also the weak limit as n x-> of a probability measure distributed equally over the dn nth inverse images of almost any point. We shall prove the following: