二维三次映射的混沌动力学

Chaotic dynamics for two dimensional cubic mapping

为了研究二维三次映射的混沌动力学,运用Moser定理和多项式零点斜率的性质,证明映射存在Smale马蹄,并且映射在不变集上拓扑共轭于三符号动力系统.计算不动点和2周期点的Lyapunov指数谱表明,它们的最大Lyapunov指数均大于零.

Chaotic dynamics was investigated for a class of two dimensional cubic mapping.By Moser′s theorem,as well as the derivative properties on zeros of polynomial,the Smale horseshoe was proved for the two dimensional cubic mapping.Moreover,the cubic mapping on horseshoe was showed topologically conjugate to the shift map on sequence space of three symbols.The largest Lyapunov exponents at the fixed points and two periodic points were proved to be all positive.