Degeneration of the Julia set to singular loci of algebraic curves

Abstract

We show that, when a non-integrable rational map changes to an integrable one continuously, a large part of the Julia set of the map approach indeterminate points (IDP) of the map along algebraic curves. We will see that the IDPs are singular loci of the curves. C 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Singularity Confinement and Projective Resolution of Triangulated Category

“…Moreover in our recent paper [28] we have shown, by studying a simple map of 2 dimension, how the Julia set approach to VSP. We have found that the periodic points move along an algebraic curve for each period as a changes its value.…”

“…we see that D(ij, kl) is an isomorphism. Since corners connected by an edge have a common suffix, (28) simplifies…”