Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE MEASURE OF THE UNIFORMLY HYPERBOLIC INVARIANT SET OF EXACT SEPARATRIX MAP

  • Kim, Gwang-Il (Department of Mathematics, Gyeongsang National University) ;
  • Chi, Dong-Pyo (Department of Mathematics, Seoul National University)
  • Published : 1997.07.01
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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 Hamilitonian 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

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