A priori bounds for boundedprimitive renormalization
A priori bounds for boundedprimitive renormalization

Jeremy Kahn, SUNY at Stony Brook
Fine Hall 401
We say that an infinitely renormalizable quadratic polynomial has boundedprimitive type if we can find an infinite sequence of primitive renormalization times, such that the ratio between consecutive terms of the sequence is bounded. We prove that any such polynomial has the a priori bounds: there is a lower bound on the modulus of all renormalizations. This implies that the Mandelbrot set is locally connected at the associated parameter values.