Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 4
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- Pages.857-872
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON THE BIGTH OF PB-CHAINS FOR GENERAL AREA-PRESERVING MAPS
- Kim, Yong-In (Department of Mathematics, University of Ulsan, Ulsan 680-749)
- Published : 1994.10.01
Abstract
A PB-chain(Poincare-Birkhoff chain) is by definition a pair of elliptic and hyperbolic n-periodic orbits for a mapping and its existence has been well established numerically or analytically in many particular occasions such as in standard maps or twist maps [1, 8, 9] or Henon maps [1, 2, 12]. This paper gives focus on the investigaton of the appearance of such a PB-chain in a one-parameter family of general area-preserving maps and is in fact a generalization of the results given in [12] for a one-parameter family of specific area-preserving maps, so called Henon maps.
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