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Complex dynamics
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<p>Complex dynamics, or holomorphic dynamics, is the study of <a href="/facts/Dynamical_system/782gREl5">dynamical systems</a> obtained by <a href="/facts/Iterated_function/Vzsx64An">iterating</a> a <a href="/facts/Complex_analytic/hgCoQlH0">complex analytic</a> mapping. This article focuses on the case of algebraic dynamics, where a <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> or <a href="/facts/Rational_function/2nJGu0Ko">rational function</a> is iterated. In geometric terms, that amounts to iterating a mapping from some <a href="/facts/Algebraic_variety/Vk7f97vn">algebraic variety</a> to itself. The related theory of <a href="/facts/Arithmetic_dynamics/11Ir59ko">arithmetic dynamics</a> studies iteration over the <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> or the <a href="/facts/P-adic_number/SDgDbkLF">p-adic numbers</a> instead of the <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a>. </p>