Memoires de la Societe Mathematique de France
Volume: 121;
2010;
139 pp;
Softcover
MSC: Primary 32; 58;
Print ISBN: 978-2-85629-301-0
Product Code: SMFMEM/121
List Price: $42.00
AMS Member Price: $33.60
A Fundamental Domain for \(V_{3}\)
Share this pageMary Rees
A publication of the Société Mathématique de France
The author describes a fundamental domain for the punctured Riemann surface \(V_{3,m}\) which parametrises (up to Möbius conjugacy) the set of quadratic rational maps with numbered critical points, such that the first critical point has period three and the second critical point is not mapped in \(m\) iterates or less to the periodic orbit of the first. This gives, in turn, a description, up to topological conjugacy, of all dynamics in all type III hyperbolic components in \(V_{3}\), and gives indications of a topological model for \(V_{3}\), together with the hyperbolic components contained in it.
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Readership
Graduate students and research mathematicians interested in pure mathematics.