Cheraghi, Davoud (2013) Typical orbits of quadratic polynomials with a neutral fixed point : Brjuno Type. Communications in Mathematical Physics, Volume 322 (Number 3). pp. 999-1035. doi:10.1007/s00220-013-1747-5 ISSN 0010-3616.

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Abstract

We describe the topological behavior of typical orbits of complex quadratic polynomials Pα(z)=e2παiz+z2, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Communications in Mathematical Physics
Publisher:	Springer
ISSN:	0010-3616
Official Date:	September 2013
Dates:	Date Event September 2013 Published
Volume:	Volume 322
Number:	Number 3
Page Range:	pp. 999-1035
DOI:	10.1007/s00220-013-1747-5
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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