Analytical studies of irrationally indifferent cycles in higher dimensional complex dynamics and Nevanlinna theory

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We obtained the finiteness and vanishig of the nonlinearity of finite morphisms on projective space over more general fields than complex numbers, and applied it to singular domains in complex dynamics in higher dimensions. Moreover, under the positivity of Lyapunov exponents, we obtained a partial affirmative answer for repelling density problem in non-archimedean dynamics by establishing the approximation formula of Lyapunov exponents.