✦ LIBER ✦
Recurrent critical points and typical limit sets for conformal measures
✍ Scribed by Alexander M. Blokh; John C. Mayer; Lex G. Oversteegen
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 122 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
For a rational f : C → C with a conformal measure µ we show that if there is a subset of the Julia set J (f ) of positive µ-measure whose points are not eventual preimages of critical or parabolic points and have limit sets not contained in the union of the limit sets of recurrent critical points, then µ is non-atomic, µ(J (f )) = 1, ω(x) = J (f ) for µ-a.e. point x ∈ J (f ) and f is conservative, ergodic and exact. The proof uses a version of the Lebesgue Density Theorem valid for Borel measures and conformal balls.