Dimension of Phase Point Trajectory

Kun Yao
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Abstract

In a physical system, phase point trajectory is impossible to be space-filling curve, of which the dimension is not greater than one. Equipotential map concept is proposed. When phase point trajectory dimension is 0, calculus tool is no longer applicable. System state can be changed instantly. When phase point trajectory dimension is 1, differential equation can be used to handle this case.
相点轨迹的尺寸
在物理系统中,相点轨迹不可能是维数不大于1的空间填充曲线。提出了等势映射的概念。当相点轨迹维数为0时,微积分工具不再适用。系统状态可以瞬间改变。当相点轨迹维数为1时,可以用微分方程来处理这种情况。
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