Fractal Dimension for Fractal Structures

Released on by Manuel Fernández-Martínez
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  • Fractal Dimension for Fractal Structures Book Detail

  • Author : Manuel Fernández-Martínez
  • Release Date : 2019-04-23
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 217
  • ISBN 13 : 3030166457
  • File Size : 49,49 MB
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Fractal Dimension for Fractal Structures by Manuel Fernández-Martínez PDF Summary

Book Description: This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.

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Fractal Dimension for Fractal Structures

Fractal Dimension for Fractal Structures

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This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure