标度对称性

Scaling Symmetry

标度对称性是无特征尺度现象的主要特征。海岸线、湍流、临界相变等问题中都有。对动力系统作标度变换可以找出不变量。在混沌模型中从自相似变换中找出了Ｆｅｉｇｅｎｂａｕｍ常数这个有意义的不变量。在气候资料中冷暖是随时间尺度而变化的，但也存在不变量。标度对称性在数学上可以看成是不断重复的迭代映射，在生物学上可以看成是像兔子繁殖一样的Ｆｉｂｏｎａｃｃｉ数的自我复制。

The scaling symmetry is elementary characteristic of characterless scale phenomena such as length of the coast,tubulence,critical phase transitions.The scaling Symmetry is to seek after invariance under scale transformation for dynamical system.The Fiegenbaum constant is a famous invariance via period doubling scaling transformation for chaotic system.The climatic colding and warming change with time scale,but there is also invariance.In mathematically the scaling symmetry may be considered as a interated map,in biologically as a self reproduction.The self simitarity of scale transformation is related to spiral structure in nature.