An Invitation to Fractal Geometry: Fractal Dimensions, Self-similarity, and Fractal Curves - Couverture rigide

Lapidus, Michel L.; Radunovic, Goran

 
9781470476236: An Invitation to Fractal Geometry: Fractal Dimensions, Self-similarity, and Fractal Curves
Couverture rigide
ISBN 10 : 1470476231 ISBN 13 : 9781470476236
Editeur : American Mathematical Society, 2025

Synopsis

This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Targeting undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Michel L. Lapidus, University of California, Riverside, CA, and Goran Radunovic, University of Zagreb, Croatia

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2025
Langue
anglais
ISBN 10 
1470476231
ISBN 13 
9781470476236
Reliure
Relié
Nombre de pages
611
Coordonnées du fabricant
non disponible
Personne responsable
non disponible