Differentiability of the minimal average action as a function of the rotation number |
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Authors: | John N Mather |
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Institution: | (1) Princeton University, Fine Hall, Washington Rd, 08544 Princeton, NJ, USA |
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Abstract: | Let
be a finite composition of exact twist diffeomorphisms. For any real number , letA() denote the minimal average action of
-invariant measures with angular rotation number . We prove thatA() is differentiable at every irrational number and that for generic
it is not differentiable at rational , thus verifying conjectures of S. Aubry. Moreover, we show that these results are valid for a variational principleh which satisfies the condition which we have called elsewhere (H). As a consequence, we generalize a result due to Bangert concerning geodesics on a two dimensional torus with an arbitrary, but sufficiently smooth metric.supported by NSF grant no. DMS-8806067.01 and a Guggenheim Fellowship. |
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Keywords: | |
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