# American Institute of Mathematical Sciences

July  2005, 12(4): 773-789. doi: 10.3934/dcds.2005.12.773

## 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, Mexico 2 Instituto de Matemáticas, Unidad Cuernavaca. UNAM, Av. Universidad s/n. Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico 3 Facultad de Ciencias, UNAM, Av. Universidad 30, C.U., México D.F., C.P. 04510, Mexico

Received  May 2003 Revised  September 2004 Published  January 2005

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.
Citation: Patricia Domínguez, Peter Makienko, Guillermo Sienra. Ruelle operator and transcendental entire maps. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 773-789. doi: 10.3934/dcds.2005.12.773
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