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http://dx.doi.org/10.7858/eamj.2014.038

DYNAMICS ON AN INVARIANT SET OF A TWO-DIMENSIONAL AREA-PRESERVING PIECEWISE LINEAR MAP  

Lee, Donggyu (Gyeongju high School)
Lee, Dongjin (Gyeongju high School)
Choi, Hyunje (Gyeongju high School)
Jo, Sungbae (Gyeongju high School)
Publication Information
East Asian mathematical journal / v.30, no.5, 2014 , pp. 583-597 More about this Journal
Abstract
In this paper, we study an area-preserving piecewise linear map with the feature of dangerous border collision bifurcations. Using this map, we study dynamical properties occurred in the invariant set, specially related to the boundary of KAM-tori, and the existence and stabilities of periodic orbits. The result shows that elliptic regions having periodic orbits and chaotic region can be divided by smooth curve, which is an unexpected result occurred in area preserving smooth dynamical systems.
Keywords
Dangerous border collision bifurcnation; stability of fixed points; stable and unstable manifolds;
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