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8 - Selected Topics from Complex Analysis

from Part II - Complex Analysis, Conformal Measures, and Graph Directed Markov Systems

Published online by Cambridge University Press:  20 April 2023

Janina Kotus  and
Mariusz Urbański
Janina Kotus
Affiliation:
Warsaw University of Technology
Mariusz Urbański
Affiliation:
University of North Texas
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Summary

In this chapter we encounter for the first time in the book holomorphic dynamics. Its settings are somehow technical and it has, on the one hand, a very preparatory character serving the needs of constructing and controlling Sullivan's conformal measures in various subsequent parts of the book; already in the next chapter. On the other hand, this chapter is important and interesting on its own. Indeed, its hypotheses are very general and flexible, and under such weak assumptions it establishes in the context of holomorphic dynamics such important results as Pesin's Theory, Ruelle's Inequality, and Volume Lemmas.

Keywords

holomorphic dynamicsPesin's TheoryRuelle's Inequality Volume LemmasMãné’s partition
Type
Chapter
Information
Meromorphic Dynamics
Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures
 , pp. 249 - 315
Publisher: Cambridge University Press
Print publication year: 2023

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