- 91-27 Falcolini C., de la Llave R.
- A rigorous partial justification of Greene's criterion
(90K, Plain TeX)
Sep 17, 91
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Abstract. We prove several theorems that give support to Greene's
criterion for existence or not of invariant circles in twist maps.
In particular, we show that some of the implications
of the criterion are correct when the
Aubry-Mather sets are smooth invariant circles or uniformly hyperbolic.
We also suggest a simple modification that can work
in the case that the Aubry-Mather sets have non-zero Lyapunov exponents.