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For an entire function let be the Newton function associated to . Each zero of is an attractive fixed point of and is contained in an invariant component of the Fatou set of the meromorphic function in which the iterates of converge to . If has an asymptotic representation , in a sector , then there exists an invariant component of the Fatou set where the iterates of tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...
Let Q be the unit square in the plane and h: Q → h(Q) a quasiconformal map. When h is conformal off a certain self-similar set, the modulus of h(Q) is bounded independent of h. We apply this observation to give explicit estimates for the variation of multipliers of repelling fixed points under a "spinning" quasiconformal deformation of a particular cubic polynomial.
Given a holomorphic mapping of degree we give
sufficient conditions on a positive closed (1,1) current of of unit mass under which
converges to the Green current as . We also conjecture
necessary condition for the same convergence.
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