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Bifurcation currents and equidistribution in parameter space. (English) Zbl 1405.37003

Bonifant, Araceli (ed.) et al., Frontiers in complex dynamics. In celebration of John Milnor’s 80th birthday. Based on a conference, Banff, Canada, February 2011. Princeton, NJ: Princeton University Press (ISBN 978-0-691-15929-4/hbk; 978-1-400-85131-7/ebook). 515-566 (2014).
Summary: We review the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on \(\mathbb{P}^1\) or subgroups of the Möbius group PSL\((2,\mathbb{C}))\). 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.
For the entire collection see [Zbl 1285.37001].

MSC:

37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F75 Dynamical aspects of holomorphic foliations and vector fields
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