Home » Views of Parameter Space by Mary Rees
Views of Parameter Space Mary Rees

Views of Parameter Space

Mary Rees

Published May 10th 2004
ISBN : 9782856291443
Paperback
418 pages
Enter the sum

 About the Book 

In this work, the author investigates the structure of certain parameter spaces. The aim is to understand the variation of dynamics--in particular, of hyperbolic dynamics--in certain parameter spaces of rational maps. In order to do this, sheMoreIn this work, the author investigates the structure of certain parameter spaces. The aim is to understand the variation of dynamics--in particular, of hyperbolic dynamics--in certain parameter spaces of rational maps. In order to do this, she examines the topological and geometric structure of larger parameter spaces, of branched coverings of the Riemann sphere ${/overline {/mathbf C}}$, where some of the critical points are constrained to have finite forward orbits.pObtained is a complete topological description of the spaces under consideration, from two points of view, which are called the Topographers View and the Residents View. The Topographers View is, in essence, a geometrizing theorem. It shows that the space in question is, up to homotopy equivalence, a countable union of disjoint geometric pieces, joined together by handles. The most typical geometric pieces are varieties of rational maps and tori. The Residents View is a view of the whole parameter space from the dynamical plane of a map (a resident) in the parameter space. This is necessarily a two-dimensional view, in which the geometric pieces of the parameter space appear as disjoint convex regions in the dynamical plane.