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A topological invariant for volume preserving diffeomorphisms

Published online by Cambridge University Press:  19 September 2008

Jean-Marc Gambaudo  and
Elisabeth Pécou
Jean-Marc Gambaudo
Affiliation:
Institut Non Linéaire de Nice, UMR CNRS 129, 1361, route des lucioles, 06560 Valbonne, France
Elisabeth Pécou
Affiliation:
Institut Non Linéaire de Nice, UMR CNRS 129, 1361, route des lucioles, 06560 Valbonne, France
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 3 , June 1995 , pp. 535 - 541
Copyright
Copyright © Cambridge University Press 1995

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References

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