Kawakami映射的超混沌行为研究

通过对一类平面二维映射系统非线性动力学行为的分析，发现该系统存在一个奇怪吸引子，该吸引子具有两个正Lyapunov指数和分数维。通过该系统不动点的分析揭示了该吸引子的吸引域边界结构，即不稳定第二类结点与不稳定偶数周期点在吸引域边界上的相间排列。

STUDY ON STRANGE HYPER-CHAOTIC DYNAMICS OF KAWAKAMI MAP

The strange hyper-chaotic dynamics of several noninvertibletwo-dimensional map systems with two positive Lyapunov exponents arestudied in this paper. These systems have spreading attractors. As anexample the Kawakami map is studied more thorough. The characters of thefixed points, chaotic attractor and attractive basin are analyzed. Thephenomena that the second unstable node is on the attractive basinboundary and the structure that the even unstable periodic points arearranged on the boundary is found and analyzed. The second unstable nodeand the unstable even periodic points and their stable flow are arrangedon the boundary of the attractive basin. This structure especially withthe second node is reported and studied rarely. The dynamics of ndimensional map yielding n positive Lyapunov exponents is onlydetailedly studied for the case of n=1 before. The results in this papershow that such a situation can be met for n=2. The attractors spread ina zone with complicate structure. This is different from the commonstrange attractors contract to a low dimensional manifold like H`enonmap. Because the attractor of Kawakami map also has a non-integerdimension, the geometry structure in state plane should be strange. Aconclusion can be drawn, if a two-dimensional map has only two unstablefixed point, a node and a focus, and there is a attractive setsurrounding the focus, the attractive set must have a bounded attractivebasin and the unstable node on the boundary. If the node is unstable secondnode, there must be even periodic point on the boundary.