TL;DR
This paper explains the method of sausages, a way to decompose the shift locus of normalized polynomials into complex algebraic varieties, highlighting its structure and implications.
Contribution
It provides an expository overview of the sausages method and its consequences for understanding the shift locus in complex dynamics.
Findings
Decomposition of the shift locus into codimension 0 submanifolds
Each submanifold is homeomorphic to a complex algebraic variety
Clarification of the structure of the shift locus
Abstract
The shift locus is the space of normalized polynomials in one complex variable for which every critical point is in the attracting basin of infinity. The method of sausages gives a (canonical) decomposition of the shift locus in each degree into (countably many) codimension 0 submanifolds, each of which is homeomorphic to a complex algebraic variety. In this paper we explain the method of sausages, and some of its consequences. This is an expository paper.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Polynomial and algebraic computation