Ruelle operator and transcendental entire maps

Patricia Domínguez; Peter Makienko; Guillermo Sienra

doi:10.3934/dcds.2005.12.773

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2005, Volume 12, Issue 4: 773-789. Doi: 10.3934/dcds.2005.12.773

This issue Previous Article Decoupling techniques for wave equations with dynamic boundary conditions Next Article Wave propagation and blocking in inhomogeneous media

Ruelle operator and transcendental entire maps

1.
F.C. Físico-Matemáticas, B.U.A.P, Av. San Claudio, Col. San Manuel, C.U., Puebla Pue., C.P. 72570
2.
Instituto de Matemáticas, Unidad Cuernavaca. UNAM, Av. Universidad s/n. Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos
3.
Facultad de Ciencias, UNAM, Av. Universidad 30, C.U., México D.F., C.P. 04510

Received: May 2003

Revised: September 2004

Published: July 2005

Abstract / Introduction Related Papers Cited by

Abstract

We calculate the Ruelle operator of a transcendental entire function $f$ having only a finite set of algebraic singularities. Moreover, under certain topological conditions on the postcritical set we prove (i) if $f$ has a summable critical point, then $f$ is not structurally stable and (ii) if all critical points of $f$ belonging to Julia set are summable, then there do not exist invariant lines fields on the Julia set.

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Mathematics Subject Classification: 37F10, 37F45.

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