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Remarks on the Ruelle operator and the invariant line fields problem: II

Published online by Cambridge University Press:  26 August 2005

PETER M. MAKIENKO
PETER M. MAKIENKO
Affiliation:
Instituto de Matematicas, Av. de Universidad s/N., Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico and Institute for Applied Mathematics, 9 Shevchenko str., Khabarovsk, Russia (e-mail: makienko@aluxe.matcuer.unam.mx, makienko@iam.khv.ru)
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Abstract

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Let R be a rational map. A critical point c is called summable if the series $\sum_i(1/(R^i)'(R(c)))$ is absolutely convergent. Under certain topological conditions on the postcritical set we prove that R cannot be structurally stable if it has a summable critical point $c \in J(R)$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 5 , October 2005, pp. 1561 - 1581
Copyright
2005 Cambridge University Press