The Geometry of Fractal Sets

K. J. Falconer (Autor)

Buch | Softcover

180 Seiten

1986
Cambridge University Press (Verlag)
978-0-521-33705-2 (ISBN)

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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.

Preface; Introduction; Notation; 1. Measure and dimension; 2. Basic density properties; 3. Structure of sets of integral dimension; 4. Structure of sets of non-integral dimension; 5. Comparable net measures; 6. Projection properties; 7. Besicovitch and Kakeya sets; 8. Miscellaneous examples of fractal sets; References; Index.

Erscheint lt. Verlag	24.7.1986
Reihe/Serie	Cambridge Tracts in Mathematics
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	154 x 228 mm
Gewicht	270 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-521-33705-4 / 0521337054
ISBN-13	978-0-521-33705-2 / 9780521337052
Zustand	Neuware