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Complex dynamics
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===Examples=== * For the mapping <math>f(z)=z^2</math> on <math>\mathbf{CP}^1</math>, the equilibrium measure <math>\mu_f</math> is the [[Haar measure]] (the standard measure, scaled to have total measure 1) on the unit circle <math>|z|=1</math>. * More generally, for an integer <math>d>1</math>, let <math>f\colon \mathbf{CP}^n\to\mathbf{CP}^n</math> be the mapping ::<math>f([z_0,\ldots,z_n])=[z_0^d,\ldots,z_n^d].</math> :Then the equilibrium measure <math>\mu_f</math> is the Haar measure on the ''n''-dimensional [[torus]] <math>\{[1,z_1,\ldots,z_n]: |z_1|=\cdots=|z_n|=1\}.</math> For more general holomorphic mappings from <math>\mathbf{CP}^n</math> to itself, the equilibrium measure can be much more complicated, as one sees already in complex dimension 1 from pictures of Julia sets.
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