1. Arnol’d says’ incoming manifold’ and’ outgoing manifold’, which is more intuitive and less easily lends itself to confusion.
2. Theorem 7.1 is due to the American Philip H(UPARTMAN) (1960). Theorem 7.2 is due independently to H(UPARTMAN) and to the Russian mathematician D.GROBMAN (1959). The best proof is that due to Charles P(UPUGH), for which see [IR] pp. 113-119, [PM] pp. 60-67 or [RO] §5.7.