Characteristic Exponents of Rational Functions
Anna Zdunik
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014), p. 257-263 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:281195 
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     year = {2014},
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Anna Zdunik. Characteristic Exponents of Rational Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 257-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-3-6/