一例从保守向类耗散的过渡

A transition from conservative to quasi-dissipative

建议研究一类特殊的分段连续力场中的受击转子 .它在一个控制参数连续改变时可以演示从分段连续保守系统向类耗散系统的连续过渡 ,从而展现不连续边界像集随机网向一个瞬态随机网 ,以及网上的无边界混沌扩散运动向局域规则运动的转变 .这种转变可能用瞬态随机网的分数维随控制参数的对数改变规律来描述 。

A special kicked rotor moving in a piecewise continuous force field is suggested and studied. When adjusting a control parameter,the rotor displays a transition from conservative to quasi-dissipative, and a change of a stochastic web formed by the set of the images of the discontinuous borderlines to a transient stochastic web. This transition and change can be described by a logarithmic rule of the fractal dimension of the transient stochastic web versus the control parameter, or a rule of the averaged lifetime of the iterations in the transient stochastic web versus the control parameter.