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I Choas and conservation

  1. May 6, 2016 #1
    I was reading a Steven Strogatz book and he said that the self similarity of fractals is a symmetry. Has any conservation law been linked to this type of symmetry using Noether's Theorem?
     
  2. jcsd
  3. May 6, 2016 #2
    One needs to distinguish between physical symmetries and mathematical symmetries.

    Noether's Thm can be stated informally as:

    If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

    I haven't read the Strogatz book, but two questions that come to mind are:

    Is the purported symmetry in fractals a continuous symmetry?

    Is the purported symmetry in fractals a physical symmetry (really a perfect symmetry in a physical realization)?

    A lot of purported symmetries in physical systems are neither exact nor continuous.
     
  4. May 6, 2016 #3

    Andy Resnick

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    This is at the edge of my understanding: scale invariance (self similarity) is associated with conformal symmetry:

    https://en.wikipedia.org/wiki/Conformal_symmetry

    These are typically associated with phase transitions, but I think you can also generate a conserved energy-momentum tensor from this.
     
  5. May 6, 2016 #4
    perfect, thanks
     
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