Fractal concepts in surface growth.

*(English)*Zbl 0838.58023
Cambridge: Cambridge Univ. Press. xx, 366 p., £45.00; $ 69.95/hbk (1995).

As a textbook on the use of fractals in surface growth for a course in surface science or engineering, this book contains an account of the subject that is both lucid and interesting. The book is illustrated with a large number of well-drawn diagrams and well-reproduced photographs. Its typographic design is excellent and for a technical book of its length and size it is, at least in the paperback version, very reasonably priced. There is a relatively small amount of mathematics in the text where it is mainly used as a language to describe the quantitative behaviour of fractal objects.

The mathematics in the book is weak in that it lacks a large number of appropriate definitions and the deductive thread is so thin that often it is almost invisible. Nevertheless, mathematicians will find here a large number of examples of how mathematical methods developed for the study of fractal geometry are used in the physical sciences. This is primarily a textbook meant for science and engineering students and as such is very probably an unqualified success. It has an almost comprehensive collection of references to the recent works on fractals with 508 entries in the bibliography.

The mathematics in the book is weak in that it lacks a large number of appropriate definitions and the deductive thread is so thin that often it is almost invisible. Nevertheless, mathematicians will find here a large number of examples of how mathematical methods developed for the study of fractal geometry are used in the physical sciences. This is primarily a textbook meant for science and engineering students and as such is very probably an unqualified success. It has an almost comprehensive collection of references to the recent works on fractals with 508 entries in the bibliography.

Reviewer: C.S.Sharma (London)

##### MSC:

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

00A79 | Physics |

28A80 | Fractals |

58Z05 | Applications of global analysis to the sciences |

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

74G70 | Stress concentrations, singularities in solid mechanics |

74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |

60K40 | Other physical applications of random processes |

81Q50 | Quantum chaos |

82B28 | Renormalization group methods in equilibrium statistical mechanics |