Critical point theory in knot complements

Given a Morse function defined in the complement of a knot K subset of R-3 we obtain a lower bound for the number of its critical points, depending on a knot invariant t(K) known as the "tunnel number". This lower bound is used to prove existence of many periodic solutions in a system of differential equations from celestial mechanics. (C) 2014 Elsevier B.V. All rights reserved.