Abstract

 The Thurston pullback map induced by a surface homeomorphism is introduced by Thurston in his famous work about classification of surface homeomorphisms. In 1980s, he applied the pullback map induced by a marked branched covering of the sphere to characterize the dynamics of rational maps. Later, there are many works to study the relation of dynamics of ratinal maps and  Thurston pullback maps. In this talk, I will focus on the classification of rational maps with constant Thurston pullback map.  We will present a new class of such maps and give a complete description in case of regular marked polynomials. This is a joint work with Yiran Wang.