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Infinitesimal perturbations of rational maps

arXiv:math/0109172 · doi:10.1088/0951-7715/15/3/310

Abstract

We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.

10 pages, no figures, third version. To appear in Nonlinearity