The geometry of fractal sets /

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various direct...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser:
Falconer, K. J.
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
Cambridge : Cambridge University Press, 1985.
Zusammenfassung:
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
Umfang:
1 online resource (xiv, 162 pages) : digital, PDF file(s).
Anmerkungen:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
ISBN:
9780511623738 (ebook)
DOI:
10.1017/CBO9780511623738
Schlagworte:
Fractals.
Geometric measure theory.
Bezugswerke:
Links: