Let M be a complex Hermitian manifold and {fa}a∈D a holomorphic family of endomorphisms of M, where D is the unit disk. This means that the map D × M → M, defined by (a, x) → fa(x), is holomorphic. Suppose that f = f_0 has com- Pact surjectively invariant subset K, that is, f(K) = K. For example, K could be A fixed point or a periodic orbit, but also a more complicated set such as the Julia Set of a rational function. We may then ask if K is persistent under the perturba- Tion fa of the map f.
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