Rescaling limits of complex rational maps

Abstract

We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space.It is shown that any given sequence of maps of degree $d\ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which are not postcritically finite. For quadratic rational maps, a complete description of the possible rescaling limits is given. These results are obtained employing tools from non-Archimedean dynamics.

References in corpus (1)

• Topology and Geometry of the Berkovich Ramification Locus for Rational Functions, II

Cited by in corpus (13)

• Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability
• Dynamics on Trees of Spheres
• Limits of rational maps, R-trees and barycentric extension
• On hyperbolic rational maps with finitely connected Fatou sets
• Arbitrary large number of non trivial rescaling limits
• On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
• Iteration at the Boundary of Newton Maps
• Berkovich spaces and Deligne-Mumford compactification
• On geometrically finite degenerations I: boundaries of main hyperbolic components
• Indeterminacy loci of iterate maps in moduli space
• A Riemannian metric on polynomial hyperbolic components
• Degenerations of Complex Dynamical Systems
• Compactifications of the moduli spaces of Newton maps