Anti-holomorphic dynamics and parameter spaces of polynomials
speaker: SABYASACHI MUKHERJEE (JACOBS UNIVERSITY BREMEN)abstract: We will study the connectedness loci of degree dunicritical antipoly- nomials f(z) = ¯ z+ c, known as the Multicorns. Although the iteration theory of anti-polynomials differs only in a few subtle ways from that of ordinary polynomials, the parameter spaces of unicritical anti-polynomials are quite different from their holomorphic counterparts. In fact, they share many properties with the parameter spaces of polynomials with two infinite critical orbits. After stating a few known results, we will describe some combinatorial aspects of anti-holomorphic dynamics and use them to study the combina- torics and bifurcation phenomena of the Multicorns. In analogy with the cubic polynomials, there will be an example of discontinuity of landing points of periodic dynamical rays. Time permitting, we will address the question of J-stability of parabolic parameters in a transversal direction.
timetable:
Tue 15 Oct, 17:15 - 17:45, Aula Dini
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