Master Teapots and Entropy Algorithms for the Mandelbrot set


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January 27, 2022 4:00 pm - 6:00 pm

Kathryn Lindsey - Boston College

The core entropy of a postcritically finite quadratic polynomial is the topological entropy of its restriction to its Hubbard tree.  Core entropy is also the logarithm of the largest eigenvalue of the matrix associated to the Markov partition of the Hubbard tree obtained by cutting the tree at the postcritical set.  Tiozzo proved that core entropy is a continuous function of external angle for the Mandelbrot set.  How do the other (non-largest) eigenvalues of the Markov transition matrix vary with external angle?  In a recent preprint, G. Tiozzo, C. Wu and I answered this question. We defined "Master Teapots" associated to principal veins in the Mandelbrot set and proved that the eigenvalues outside the unit circle move continuously while roots inside the unit circle "persist."  This talk will discuss this circle of ideas and results, and is based on joint work with G. Tiozzo and C. Wu.