Antiholomorphe Dynamische Systeme und Reelle Schnitte

• Antragsteller: Professor Dr. Dierk Schleicher
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2013 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 237518971

Antiholomorphic dynamics is the iteration of maps that are complex conjugates of holomorphic maps. The parameter dependence is then only real-analytic. John Milnor and others discovered in complex one dimensional parameter spaces interesting structures that usually appear only in complex higher dimensional spaces (and that are harder to investigate and to visualize). The underlying phenomenon is that antiholomorphic dynamics can be seen in a natural way as a one variant of prototypical dynamics of holomorphic mappings. Goal of this research project is to develop a general theory of antiholomorphic parameter spaces and to describe the combinatorial structure of the "tricorn'' (the antiholomorphic cousin of the Mandelbrot set), which is the subject of several conjectures of John Milnor and others.The investigation is subdivided into combinatorial, topological, and geometric parts that each requires different methods.

• DFG-Verfahren: Sachbeihilfen