Fractal geometry. Mathematical foundations and applications.
2nd ed.

*(English)*Zbl 1060.28005
Chichester: Wiley (ISBN 0-470-84861-8/hbk; 0-470-84862-6/pbk). xxvii, 337 p. (2003).

From the Preface to the second edition: “It is thirteen years since “Fractal geometry – Mathematical foundations and applications” (see Zbl 0689.28003) was first published. In the meantime, the mathematics and applications of fractals have advanced enormously, with an ever-widening interest in the subject at all levels. The book was originally written for those working in mathematics and science who wished to know more about fractal mathematics. Over the past few years, with changing interests and approaches to mathematics teaching, many universities have introduced undergraduate and postgraduate courses on fractal geometry, and a considerable number have been based on parts of this book.

Thus, this new edition has two main aims. First, it indicates some recent developments in the subject, with updated notes and suggestions for further reading. Secondly, more attention is given to the needs of students using the book as a course text, with extra details to help understanding, along with the inclusion of further exercises.

Parts of the book have been rewritten. In particular, multifractal theory has advanced considerably since the first edition was published, so the chapter on ‘Multifractal Measures’ has been completely rewritten. The notes and references have been updated. Numerous minor changes, corrections and additions have been incorporated, and some of the notation and terminology has been changed to conform with what has become standard usage. Many of the diagrams have been replaced to take advantage of the more sophisticated computer technology now available. Where possible, the numbering of sections, equations and figures has been left as in the first edition, so that earlier references to the book remain valid. Further exercises have been added at the end of the chapters. Solutions to these exercises and additional supplementary material may be found on the world wide web at http://www.wileyeurope.com/fractal

In 1997 a sequel, “Techniques in Fractal Geometry” (see Zbl 0869.28003) was published, presenting a variety of techniques and ideas current in fractal research. Readers wishing to study fractal mathematics beyond the bounds of this book may find the sequel helpful.”

Thus, this new edition has two main aims. First, it indicates some recent developments in the subject, with updated notes and suggestions for further reading. Secondly, more attention is given to the needs of students using the book as a course text, with extra details to help understanding, along with the inclusion of further exercises.

Parts of the book have been rewritten. In particular, multifractal theory has advanced considerably since the first edition was published, so the chapter on ‘Multifractal Measures’ has been completely rewritten. The notes and references have been updated. Numerous minor changes, corrections and additions have been incorporated, and some of the notation and terminology has been changed to conform with what has become standard usage. Many of the diagrams have been replaced to take advantage of the more sophisticated computer technology now available. Where possible, the numbering of sections, equations and figures has been left as in the first edition, so that earlier references to the book remain valid. Further exercises have been added at the end of the chapters. Solutions to these exercises and additional supplementary material may be found on the world wide web at http://www.wileyeurope.com/fractal

In 1997 a sequel, “Techniques in Fractal Geometry” (see Zbl 0869.28003) was published, presenting a variety of techniques and ideas current in fractal research. Readers wishing to study fractal mathematics beyond the bounds of this book may find the sequel helpful.”

##### MSC:

28A80 | Fractals |

28-02 | Research exposition (monographs, survey articles) pertaining to measure and integration |

28A78 | Hausdorff and packing measures |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37B99 | Topological dynamics |

37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |

54H20 | Topological dynamics (MSC2010) |