Talk page
Title:
Bounding limbs of the Mandelbrot set
Speaker:
Abstract:
The Yoccoz inequality implies that the p/q-limb of the Mandelbrot set has size O(1/q), though it is conjectured that this bound could be improved to O(1/q^2). In this talk we will show that such a bound holds for the 1/q-limbs of the Mandelbrot set. As q tends to infinity, parameters in the 1/q-limbs tend to the parabolic parameter 1/4 and high iterates of the corresponding polynomials can converge locally to transcendental Lavaurs maps, a phenomenon called parabolic implosion. We will define analogs of external rays for Lavaurs maps and use these rays to control external rays of quadratic polynomials close to z^2+1/4.
Link:
Workshop: