top
We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that if and only if f(z) is conformally conjugate to .
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 -