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Published online by Cambridge University Press: 19 September 2008
For a smooth diffeomorphism f in ℝn+2, which possesses an invariant n-torus , such that the restriction f
is topologically conjugate to an irrational rotation, we define a number which represents the way the normal bundle to the torus
asymptotically wraps around
. We prove that this number is a topological invariant among volume-preserving maps. This result can be seen as a generalization of a theorem by Naishul, for which we give a simple proof.