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Characteristic Exponents of Rational Functions

Anna Zdunik (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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 .

On fixed points of C 1 extensions of expanding maps in the unit disc

Roberto Tauraso (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for C 1 extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.

Periodic quasiregular mappings of finite order.

David Drasin, Swati Sastry (2003)

Revista Matemática Iberoamericana

The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.

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