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Séminaire de Dynamique

École polytechnique  – Centre de Mathématiques Laurent Schwartz


14h00: Yann Mary He (University of Oklahoma)

"A quantitative equidistribution of angles of multipliers of hyperbolic rational maps"


Abstract: In this talk, we will consider the angular component of multipliers of repelling cycles of a hyperbolic rational map in one complex variable. Oh-Winter have shown that these angles of multipliers uniformly distribute in the circle (-\pi, \pi]. Motivated by the sector problem in number theory, we show that for a fixed $K \gg 1$, almost all intervals of length 2\pi/K in (-\pi, \pi] contains a multiplier angle with the property that the norm of the multiplier is bounded above by a polynomial in K. This is joint work with Hongming Nie.