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Characteristic Exponents of Rational Functions

Zdunik A.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no. 3

257--263

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