Bifurcation of semialgebraic maps
Date
2014
Authors
Drendel, Jesse William, author
Bates, Daniel, advisor
Shipman, Patrick, advisor
Tavener, Simon, committee member
Antolin, Michael, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
A semi-algebraic map is a function from a space to itself whose domain and graph are unions of solutions to systems of polynomial equations and inequalities. Thus it is a very general object with many applications, some from population genetics. The isoclines of such a map are semi-algebraic sets, which enjoy many striking properties, the most consequential of which here is that there is an algorithm to compute a "cylindrical decomposition" adapted to any finite family of semi-algebraic sets. The main subject of this paper is that a cylindrical decomposition adapted to the isoclines of a semi-algebraic map partitions parameter space into a tree which isolates bifurcations.