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Journal of the London Mathematical Society 2001 63(3):673-689; doi:10.1017/S0024610701001958
© 2001 by London Mathematical Society
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© The London Mathematical Society

Parabolic Rational Maps

Nicolai Haydn and Stefano Isola

Mathematics Department, University of Southern California Los Angeles, CA 90089-1113, USA, nhaydn{at}mtha.usc.edu
Dipartimento di Matematica e Fisica, Università di Camerino via Madonna delle Carceri, 62032 Camerino, Italy, isola{at}campus.unicam.it

Received 11 August 1999. Revision received 27 March 2000.

The paper studies the dynamics of rational maps with indifferent parabolic points by comparing their dynamical properties with those of their ‘jump transformation’ which is uniformly expanding on a non-compact set with infinite Markov partition. It establishes the spectral properties of a two-variables operator-valued function associated to the jump transformation and exploits their dynamical relevance to allow the analytic properties of the pressure, the escape rate from a neighbourhood of the Julia set and the asymptotic distribution of pre-images to be studied.


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