Characteristic Exponents of Rational Functions

Anna Zdunik. "Characteristic Exponents of Rational Functions." Bulletin of the Polish Academy of Sciences. Mathematics 62.3 (2014): 257-263. <http://eudml.org/doc/281195>.

@article{AnnaZdunik2014,
abstract = {We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent $χ_a(f)$ is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent $χ_m(f)$ can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that $χ_a(f) = χ_m(f)$ if and only if f(z) is conformally conjugate to $z ↦ z^\{±d\}$.},
author = {Anna Zdunik},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {rational maps; characteristic exponents},
language = {eng},
number = {3},
pages = {257-263},
title = {Characteristic Exponents of Rational Functions},
url = {http://eudml.org/doc/281195},
volume = {62},
year = {2014},
}

TY - JOUR
AU - Anna Zdunik
TI - Characteristic Exponents of Rational Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2014
VL - 62
IS - 3
SP - 257
EP - 263
AB - We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent $χ_a(f)$ is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent $χ_m(f)$ can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that $χ_a(f) = χ_m(f)$ if and only if f(z) is conformally conjugate to $z ↦ z^{±d}$.
LA - eng
KW - rational maps; characteristic exponents
UR - http://eudml.org/doc/281195
ER -