On an analytic approach to the Fatou conjecture

Genadi Levin. "On an analytic approach to the Fatou conjecture." Fundamenta Mathematicae 171.2 (2002): 177-196. <http://eudml.org/doc/282890>.

@article{GenadiLevin2002,
abstract = {Let f be a quadratic map (more generally, $f(z) = z^d + c$, d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series $∑_\{n≥0\} 1/(fⁿ)^\{\prime \}(c)$ converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.},
author = {Genadi Levin},
journal = {Fundamenta Mathematicae},
keywords = {Fatou conjecture; measurable invariant linefield; quadratic polynomials; Julia set; hyperbolic quadratic polynomials},
language = {eng},
number = {2},
pages = {177-196},
title = {On an analytic approach to the Fatou conjecture},
url = {http://eudml.org/doc/282890},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Genadi Levin
TI - On an analytic approach to the Fatou conjecture
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 2
SP - 177
EP - 196
AB - Let f be a quadratic map (more generally, $f(z) = z^d + c$, d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series $∑_{n≥0} 1/(fⁿ)^{\prime }(c)$ converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.
LA - eng
KW - Fatou conjecture; measurable invariant linefield; quadratic polynomials; Julia set; hyperbolic quadratic polynomials
UR - http://eudml.org/doc/282890
ER -