Bifurcation of semialgebraic maps

Drendel, Jesse William, author
Bates, Daniel, advisor
Shipman, Patrick, advisor
Tavener, Simon, committee member
Antolin, Michael, committee member
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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.
2014 Summer.
Includes bibliographical references.
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