Acta Scientiarum Naturalium Universitatis Pekinensis

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Scaling Symmetry

LIU Shida, LIU Shikuo   

  1. Department of Geophysics, Peking University, Beijing, 100871
  • Received:1996-11-06 Online:1997-09-20 Published:1997-09-20


刘式达, 刘式适   

  1. 北京大学地球物理系,北京,100871

Abstract: 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.

Key words: symmetry, scaling law, self-similar, symmetry, scaling law, self-similar

摘要: 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。标度变换的自相似和自然界广泛存在的螺旋结构相联系。

关键词: 对称, 标度律, 自相似, 对称, 标度律, 自相似

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