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On the metric properties of the Feigenbaum attractor

Abstract

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.


Publication:
Journal of Statistical Physics
Pub Date:
May 1987
DOI:

10.1007/BF01007519

Bibcode:
1987JSP....47..439A
Keywords:
  • Period-doubling;
  • fractal dimensions;
  • trajectory scaling functions
full text sources
Springer
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