The measure of the uniformly hyperbolic invariant set of exact separatrix map
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 779-788
Gwang Il Kim, Dong Pyo Chi
Gyeongsang National University, Seoul National University
Abstract : In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamiltonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.
Keywords : Separatrices, stochastic layer, twist map, separatrix map, anti-integrability, uniform hyperbolicity
MSC numbers : 34C35, 58F39
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