Dimensions of structurally stable and critical strange non-chaotic attractors

L. N. C. Adamson, Andrew Osbaldestin

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Abstract

We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.
Original languageEnglish
Article number025101
Pages (from-to)1-18
Number of pages18
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number2
DOIs
Publication statusPublished - 15 Dec 2014

Keywords

  • Computational physics
  • Statistical physics and nonlinear systems
  • dimensions
  • SNA
  • renormalization
  • stable
  • critical
  • box-counting

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