Abstract
Dimension is an important concept to dynamics because it indicates the number of independent variables inherent in a motion. Assignment of a relevant dimension in chaotic dynamics is nontrivial since, not only do chaotic motions frequently lie on complicated “fractal” surfaces, but in addition, the natural probability measures associated with chaotic motion often possess an intricate microscopic structure that persists down to arbitrarily small length scales. I call such objects fractal measures;1 and arguing by example, conjecture that the typical chaotic attractor has a fractal measure.
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Farmer, J.D. (1982). Dimension, Fractal Measures, and Chaotic Dynamics. In: Haken, H. (eds) Evolution of Order and Chaos. Springer Series in Synergetics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68808-9_20
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DOI: https://doi.org/10.1007/978-3-642-68808-9_20
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