Hyperbolicity Of Local Minimal Denjoy Set

Mather prooved the existence of global minimal Denjoy set of area-preserving twist map in1982, and then he prooved the existence of local minimal Denjoy set in1985using similar method. Cheng Wei prooved the existence of long-period orbites of area-preserving twist map after Mather’s result. This article prooved the hyperbolicity of local minimal Denjoy set with rotation number in an open and dense set of IR1under the condition that the period orbites of area-preserving twist map are hyperbolic.