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Equilibrium measures for rational maps

Published online by Cambridge University Press:  19 September 2008

Artur Oscar Lopes
Artur Oscar Lopes
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9.500-Campus do Vale-91.500, Porte Alegre-RS-Brasil
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Abstract

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For a polynomial map the measure of maximal entropy is the equilibrium measure for the logarithm potential in the Julia set [1], [4].

Here we will show that in the case where f is a rational map such that f(∞) = ∞ and the Julia set is bounded, then the two measures mentioned above are equal if and only if f is a polynomial.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 3 , September 1986 , pp. 393 - 399
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

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