Bidirectional research between complex dynamics of polynomials and transcendental entire functions

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We investigated the dynamics of polynomials and transcendental entire functions both individually and bidirectionally by mainly using complex analytic methods. As a remarkable result, for a given polynomial P we constructed a transcendental entire function which has the dynamics of P as its subdynamics by quasiconformal surgery. Also as an application of this method, we constructed, for example, (1)a transcendental entire function whose Julia set is a Sierpinski carpet, (2)a transcendental entire function which has a Cremer point but whose Julia set is locally connected. These are new examples which show new phenomena which never occur for polynomial dynamics.