arXiv Analytics

Sign in

arXiv:1111.3989 [math.DS]AbstractReferencesReviewsResources

Bifurcation currents and equidistribution on parameter space

Romain Dujardin

Published 2011-11-16, updated 2012-02-07Version 2

In this paper we review the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P^1 or subgroups of the Moebius 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 on parameter space.

Comments: Revised version, 46 pages, to appear in the proceedings of the conference "Frontiers in complex dynamics (Celebrating John Milnor's 80th birthday)"
Categories: math.DS, math.CV
Subjects: 37F45, 37F30
Related articles: Most relevant | Search more
arXiv:math/0605687 [math.DS] (Published 2006-05-26)
Cubic polynomials: a measurable view on parameter space
arXiv:1512.04131 [math.DS] (Published 2015-12-13)
Combinatorial Representation of Parameter Space for Switching Systems
arXiv:2205.04994 [math.DS] (Published 2022-05-10)
Relations between Escape Regions in the Parameter Space of Cubic Polynomials

Links

Toolbox