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1 IntroductionLet M be a manifold (possibly with boundary), and f: M → M be continuous. Call aclosed invariant set A () M an adic attractor of f if it attracts almost all points (in the senseof Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system.Such an attractor A is called n-adic if the restriction f|A can be topologically conjugate then-adic system.