Mahan Mj
TIFR
April 27, 2017
Motions of limit sets: Let $\rho_n : \pi_1(S) \to PSL_2(\mathbb{C})$ be a sequence of discrete, faithful representations converging to a representation $\rho : \pi_1(S) \to PSL_2(\mathbb{C})$. We study the question: Does the dynamics of $\rho_n(\pi_1(S))$ on the Riemann sphere converge to that of $ \rho(\pi_1(S))$? We focus on the locus of chaotic dynamics, also called the limit set.
TIFR
April 27, 2017
Motions of limit sets: Let $\rho_n : \pi_1(S) \to PSL_2(\mathbb{C})$ be a sequence of discrete, faithful representations converging to a representation $\rho : \pi_1(S) \to PSL_2(\mathbb{C})$. We study the question: Does the dynamics of $\rho_n(\pi_1(S))$ on the Riemann sphere converge to that of $ \rho(\pi_1(S))$? We focus on the locus of chaotic dynamics, also called the limit set.
It is well known, thanks to celebrated work of Mane-Sad-Sullivan that for a parametrized family of quasifuchsian groups (or equivalently convex cocompact discrete surface subgroups of $PSl(2,C))$ the limit set moves holomorphically on the Riemann sphere. We shall discuss what happens when a sequence of such groups converges to a non-quasifuchsian group. A discontinuity phenomenon was discovered in joint work with Caroline Series. In further work with Ken'ichi Ohshika, we characterize when precisely these discontinuities arise.