Harmonic measure on the Julia set for polynomial-like maps |
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Authors: | Anna Zdunik |
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Affiliation: | (1) Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland, PL |
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Abstract: | For a generalized polynomial-like mapping we prove the existence of an invariant ergodic measure equivalent to the harmonic measure on the Julia set J( f). We also prove that for polynomial-like mappings the harmonic measure is equivalent to the maximal entropy measure iff f is conformally equivalent to a polynomial. Next, we show that the Hausdorff dimension of harmonic measure on the Julia set of a generalized polynomial-like map is strictly smaller than 1 unless the Julia set is connected. Oblatum 24-IV-1995 & 22-VII-1996 |
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