Ergodic theory for Markov fibred systems and parabolic rational maps
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- by Jon Aaronson, Manfred Denker and Mariusz Urbański PDF
- Trans. Amer. Math. Soc. 337 (1993), 495-548 Request permission
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
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 337 (1993), 495-548
- MSC: Primary 58F11; Secondary 28D05, 58F23, 60F05
- DOI: https://doi.org/10.1090/S0002-9947-1993-1107025-2
- MathSciNet review: 1107025