**
Below is the ascii version of the abstract for 14-4.
The html version should be ready soon.**Wolf Jung
Core entropy and biaccessibility of quadratic polynomials
(637K, pdf)
ABSTRACT. For complex quadratic polynomials, the topology of the
Julia set and the dynamics are understood from another perspective by
considering the Hausdorff dimension of biaccessing angles and the core
entropy: the topological entropy on the Hubbard tree. These quantities
are related according to Thurston. Tiozzo [arXiv:1305.3542] has shown
continuity on principal veins of the Mandelbrot set M . This result
is extended to all veins here, and it is shown that continuity with
respect to the external angle theta will imply continuity in the
parameter c . Level sets of the biaccessibility dimension are
described, which are related to renormalization. H\"older asymptotics
at rational angles are found, confirming the H\"older exponent given
by Bruin--Schleicher [arXiv:1205.2544]. Partial results towards local
maxima at dyadic angles are obtained as well, and a possible
self-similarity of the dimension as a function of the external angle is
suggested.