Topological lower bounds on the distance between area preserving diffeomorphisms |
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Authors: | Jean-Marc Gambaudo Maxime Lagrange |
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Institution: | (1) Laboratoire de Topologie UMR CNRS 5584, Université de Bourgogne, B.P. 47870-21078, Dijon Cedex, France |
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Abstract: | Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL
2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed. |
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Keywords: | Area preserving maps group of diffeomorphisms invariant metric topological invariant |
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