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A Priori Bounds for Quadratic Maps

[HYBRID WORKSHOP] Introductory Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 08, 2022 - February 17, 2022

February 11, 2022 (11:30 AM PST - 12:20 PM PST)
Speaker(s): Mikhail Lyubich (State University of New York, Stony Brook)
Location: MSRI: Online/Virtual
  • Mandelbrot set

  • Julia sets

  • a priori bounds

  • renormalization

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Secondary Mathematics Subject Classification No Secondary AMS MSC

A Priori Bounds For Quadratic Maps


"A priori bounds" provide us with a uniform geometric control of dynamical systems in all scales. Central problems of Holomorphic Dynamics, like universal self-similarity of dynamical and parameter pictures, MLC, topological structure of neutral maps, and the area problem for Julia sets, depend on such bounds. We will give an overview of advances in this problem over the past 30 years.

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A Priori Bounds For Quadratic Maps

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