Iteration at the boundary of the space of rational maps

DOI10.1215/S0012-7094-05-13015-0zbMath1183.37086arXivmath/0403078OpenAlexW2053021640MaRDI QIDQ814690

Laura DeMarco

Publication date: 7 February 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403078

zbMATH Keywords

Riemann sphererational mapdegenerate map

Mathematics Subject Classification ID

Related Items (20)

Degenerations of complex dynamical systems. II: Analytic and algebraic stability ⋮ On geometrically finite degenerations II: convergence and divergence ⋮ Quadratic rational maps with a 2-cycle of Siegel disks ⋮ Bounded hyperbolic components of bicritical rational maps ⋮ Variation of canonical height for Fatou points on \(\mathbb{P}^1\) ⋮ On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps ⋮ On hyperbolic rational maps with finitely connected Fatou sets ⋮ Perturbations of graphs for Newton maps I: bounded hyperbolic components ⋮ Quasi-adelic measures and equidistribution on ⋮ Berkovich dynamics of Newton maps ⋮ Dynamics on ℙ¹: preperiodic points and pairwise stability ⋮ Boundedness of hyperbolic components of Newton maps ⋮ Gradient property of quadratic maps ⋮ Ribbon ℝ-trees and holomorphic dynamics on the unit disk ⋮ Limits of rational maps, \(\mathbb{R}\)-trees and barycentric extension ⋮ Trees, length spectra for rational maps via barycentric extensions, and Berkovich spaces ⋮ Singular perturbations of complex polynomials ⋮ The moduli space of quadratic rational maps ⋮ Rescaling limits of complex rational maps ⋮ DEGENERATIONS OF COMPLEX DYNAMICAL SYSTEMS

Cites Work

• Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity
• The space of rational maps on \(\mathbf P^1\)
• An invariant measure for rational maps
• On the uniqueness of the maximizing measure for rational maps
• Geometry and Dynamics of Quadratic Rational Maps
• Bounded hyperbolic components of quadratic rational maps
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