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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Bifurcation currents and equidistribution in parameter space

Bifurcation currents and equidistribution in parameter space

Chapter:
(p.515) Bifurcation currents and equidistribution in parameter space
Source:
Frontiers in Complex Dynamics
Author(s):

Romain Dujardin

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0019

This chapter reviews the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P¹ or subgroups of the Möbius group PSL(2,C)). The topics covered include the construction of bifurcation currents and the characterization of their supports, the equidistribution properties of dynamically defined subvarieties of the parameter space. Emphasis will be placed as much as possible on the similarities between methods of higher-dimensional dynamics, of the study of families of rational maps, and that of Möbius subgroups. The chapter also states a number of open questions to foster further developments of this theory.

Keywords:   bifurcation currents, equidistribution, parameter space, positive currents, one-dimensional dynamics, holomorphic dynamical systems, higher-dimensional dynamics, rational maps, Möbius subgroups

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