Characteristic Exponents of Rational Functions

• Autorzy: Anna Zdunik
• Języki publikacji: EN

Abstrakty

EN

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 $z ↦ z^{±d}$.

Kategorie tematyczne

• 30D99: None of the above, but in this section
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: 62
• Numer: 3
• Strony: 257-263

Daty

wydano

2014

Twórcy

autor

Anna Zdunik

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba62-3-6