## Dynamics On Lorentz Manifolds

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We

**have**Ke (K n V.) C L, So n < di. Then dr = n < di. Then dim(T. (V.)) = d – di < d

– d.K = dim(T(V)). [] The following two results are Lemma 6.4 and Corollary 6.5 on

pp. 466– 467 of [A00a). LEMMA 2.4.4 Let V be a finite dimensional vector space

and let B, be a sequence in

**GL**(V). Let Ye End(V) be Kowalsky for the sequence

of maps A H B, ABT' : End(V) → End(V). Then Y : V → V is nilpotent. Proof. Let Y,

be a sequence in End(V) such that Y → 0 in End(V) and such that B, Y.B.' – Y. Let

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