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We generalise the semi-Riemannian Morse index theorem to elliptic systems ofpartial differential equations on star-shaped domains. Moreover, we apply ourtheorem to bifurcation from a branch of trivial solutions of semilinearsystems, where the bifurcation parameter is introduced by shrinking the domainto a point. This extends recent results of the authors for scalar equations.

A Morse-Smale index theorem for indefinite elliptic systems and bifurcation