Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ergodic theory for Markov fibred systems and parabolic rational maps

Authors: Jon Aaronson, Manfred Denker and Mariusz Urbański
Journal: Trans. Amer. Math. Soc. 337 (1993), 495-548
MSC: Primary 58F11; Secondary 28D05, 58F23, 60F05
MathSciNet review: 1107025
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A parabolic rational map of the Riemann sphere admits a non atomic $ h$-conformal measure on its Julia set where $ h = $ the Hausdorff dimension of the Julia set and satisfies $ 1/2 < h < 2$. With respect to this measure the rational map is conservative, exact and there is an equivalent $ \sigma $-finite invariant measure. Finiteness of the measure is characterised. Central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one. A theory of Markov fibred systems is developed, and parabolic rational maps are considered within this framework.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F11, 28D05, 58F23, 60F05

Retrieve articles in all journals with MSC: 58F11, 28D05, 58F23, 60F05

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society