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Projekt Druckansicht

Antiholomorphe Dynamische Systeme und Reelle Schnitte

Fachliche Zuordnung Mathematik
Förderung Förderung von 2013 bis 2016
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 237518971
 
Erstellungsjahr 2017

Zusammenfassung der Projektergebnisse

We like to think that this project satisfied the expectations we had when developing it, and in fact exceeded them in a number of most interesting directions. Antiholomorphic dynamics had been recognized quite early by John Milnor as a conceptual feature of maps respecting real symmetries (specifically, for the dynamics of real cubic polynomials), and this motivated some early work as early as the 1990’s. However, the connections to “mainstream” holomorphic dynamics were recognized by several people only as a result of this research project. So perhaps a particularly convincing way to express the success of this project is to say that it lead to collaborations with John Milnor in the context of his ongoing study of antipode-preserving rational maps, with Mikhail Lyubich and Nick Makarov (who previously did not have much contact with antiholomorphic dynamics), and Alexandre Eremenko and Walter Bergweiler realized that this research has connections to dynamical systems that are of interest beyond the holomorphic dynamics community. We are particularly pleased that the project resolved a number of long-standing conjectures, for instance about discontinuity of straightening and the dynamical difference between embedded “tricorn-like structures” (that initially were thought of as “little tricorns” in the same spirit as the ubiquitous “little Mandelbrot sets”, but our work indicates that they might all be distinct). Consequently, the work led to several publications at good to excellent journals. It might be worth mentioning, as a “publication beyond research journals”, that the DFG decided to include one of the pictures from this project in their research calendar 2014 (December picture), as well as on their new-year greeting cards.

Projektbezogene Publikationen (Auswahl)

 
 

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