TAILIEUCHUNG - Fractal geometry mathematica foundations applications falconer

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals | irLVỈ1- UNIỤERSIDRD DE CflNTOBRIfi BIBLIOTECA FRACTAL GEOMETRY Mathematical Foundations and Applications Kenneth Falconer Reader in Mathematics University of Bristol ABRIA OTECA X ICO Y- 5 Ẩ JOHN WILEY SONS Chichester New York Brisbane Toronto Singapore Copyright 1990 by John Wiley Sons Ltd. Baffins Lane Chichester West Sussex PO19 IUD England Reprinted March 1990 All rights reserved. No part of this book may be reproduced by any means or transmitted or translated into a machine language without the written permission of the publisher. Other Wiley Editorial offices John Wiley Sons Inc. 605 Third Avenue New York NY 10158-0012 USA Jacaranda Wiley Ltd . Box 859 Brisbane Queensland 4001 Australia John Wiley Sons Canada Ltd 22 Worcester Road Rexdale Ontario M9W 1L1 Canada John Wiley Sons SEA Pte Ltd 37 Jalan Pemimpin 05-04 Block B Union Industrial Building Singapore 2057 Library of Congress Cataloging-in-Publication Data Falconer K. J. 1952- Fractal geometry mathematical foundations and applications Kenneth Falconer. p. cm. Includes bibliographical references. ISBN 0 471 92287 0 I. Fractals. I. Title. 1990 514 .74-dc20 89-37981 CIP British Library Cataloguing in Publication Data . Falconer K. J. Fractal geometry. 1. Geometrical shapes I. Title 516 .15 ISBN 0 471 92287 0 Typeset by Thomson Press India Ltd Printed and bound in Great Britain by Courier International Tiptree Essex Contents Preface IX Introduction xiii Notes and references xxii PART I FOUNDATIONS Chapter 1. Mathematical background. 3 Basic set theory. 3 Functions and limits. 6 Measures and mass distributions. 10 Notes on probability theory. 16 Notes and references. 23 Exercises. 23 Chapter 2. Hausdorff measure and dimension. 25 Hausdorff measure. 26 Hausdorff dimension. 28 Calculation of Hausdorff dimension simple examples. 31 Equivalent definitions of Hausdorff dimension. 32 Finer definitions of dimension. 33 Notes and references. 34 Exercises. .

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