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MLC Along the Real Line

Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022

May 03, 2022 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Dzmitry Dudko (Stony Brook University)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

MLC Along The Real Line


The problem of local connectivity of the Mandelbrot set goes back to the 80s, and is now closely linked to the Renormalization Theory of quadratic polynomials. A key task is to establish a priori bounds (compactness) for the quadratic-like renormalization operator. Working in the near degenerate regime, we prove such bounds for maps with real combinatorics. As a consequence, real combinatorial classes are singletons on the real line. We also obtain a uniform control of the shapes of real-symmetric copies of the Mandelbrot set, as well as their universal scaling properties. Joint work in progress with Jeremy Kahn and Misha Lyubich.

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MLC Along The Real Line

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