混沌吸引子的普适转变

二维动力学映射混沌吸引子的片结构将随耗散性的减弱以普适的方式截断,最终趋于哈密顿极限。不稳定不变流形的异宿相交可以解释混沌吸引子片结构的突变行为,突变点具有普适的标度,哈密顿映射对于耗散方向的重正化理论可以给出这一普适标度。

Universal Transition of Chaotic Attractors

The band struture of chaotic attractors for two dimentional dynamical mappping is truncated in a universal way as the dissipation is reduced so that the system approaches its Hamiltonian limit. The crisis behavior of band structure of chaotic attractors can be explained by heteroclinic crises of unstable invariant manifold. There is a universal scaling law for critical crisis points which can be derived from the dissipative generalization of the Hamiltonian renormalization theory.