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We prove that every endomorphism which satisfies Axiom A and the strongtransversality conditions is $C^1$-inverse limit structurally stable. Theseconditions were conjectured to be necessary and sufficient. This result isapplied to the study of unfolding of some homoclinic tangencies. This alsoachieves a characterization of $C^1$-inverse limit structurally stable coveringmaps.

Structural stability of the inverse limit of endomorphisms