Abstract
LET h4 be a compact differentiable manifold without boundary. A Cl-endomorphism f: IV--+ M is expanding if for some (and hence any) Riemannian metric on M there exist c > 0, 1 > 1 such that ]/7’f”ul] 2 c/Z~]/U]I for all u E TM and all integers m > 0. In this paper we show that any compact manifold with a flat Riemannian metric admits an expanding endomorphism. The classification of expanding endomorphisms, up to topological conjugacy, was studied in [3]. It is of interest not only abstractly but also because the inverse limit of an expanding endomorphism can be considered as an indecomposable piece of the non-wandering set of diffeomorphism: see [4] and [5].
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