Harmonic measure on the Julia set for polynomial-like maps
- Anna ZdunikAffiliated withInstitute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- Harmonic measure on the Julia set for polynomial-like maps
Volume 128, Issue 2 , pp 303-327
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Anna Zdunik (A1)
- Author Affiliations
- A1. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland, PL