Perspectives on Parabolic Points in Holomorphic Dynamics (15w5082)


(Institut de Mathématiques de Toulouse)

Adam L. Epstein (Warwick University)

(Roskilde University)


The Banff International Research Station will host the "Perspectives on Parabolic Points in Holomorphic Dynamics (HALF)" workshop from March 29th to April 3rd, 2015.

Holomorphic Dynamics studies structures arising from iteration on complex analytic manifolds.
Maps of interest often arise in natural families.
The dynamics of a map may be compared with that of nearby maps,
and the parameters where this dependence is discontinuous constitute the bifurcation locus of the family.
For example, the boundary of the Mandelbrot set is the bifurcation locus of a one-parameter family
of quadratic polynomial maps of the complex plane.
The backbone of the bifurcation locus of any reasonable family of holomorphic dynamical systems
consists of those maps with one or more parabolic orbits,
that is, cycles whose dynamical multipliers are roots of unity.
Adrien Douady's parabolic implosion theory is a fundamental tool, not only for studying such bifurcations,
but also for exploiting them, to exhibit subtle examples and to prove deep theorems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).