{"product_id":"an-invitation-to-fractal-geometry-fractal-dimensions-self-similarity-and-fractal-curves-hardback-9781470476236","title":"An Invitation to Fractal Geometry; Fractal Dimensions, Self-Similarity, and Fractal Curves (Hardback) 9781470476236","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Invitation to Fractal Geometry\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eFractal Dimensions, Self-Similarity, and Fractal Curves\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichel L. Lapidus (Author), Goran Radunovic (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470476236\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e611 pages\u003cbr\u003e25.4 x 17.8 x 3.8 cm, 1.268 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003ePreliminary material\u003c\/li\u003e\n\u003cli\u003eIntroduction to concepts in fractal geometry\u003c\/li\u003e\n\u003cli\u003eMetric spaces and fixed point theorem\u003c\/li\u003e\n\u003cli\u003eMeasure theory and integrals\u003c\/li\u003e\n\u003cli\u003eDimension theory\u003c\/li\u003e\n\u003cli\u003eIterated function systems and self-similarity\u003c\/li\u003e\n\u003cli\u003eIntroduction to Hausdorff measure and dimension\u003c\/li\u003e\n\u003cli\u003e$\\delta$-Approximate Hausdorff measures, via Caratheodory's theory\u003c\/li\u003e\n\u003cli\u003eConstruction and properties of Hausdorff measure\u003c\/li\u003e\n\u003cli\u003eMinkowski content and Minkowski dimension\u003c\/li\u003e\n\u003cli\u003eFractal curves and their complex dimensions\u003c\/li\u003e\n\u003cli\u003eEpilogue: A primer of fractal curves and their complex dimensions\u003c\/li\u003e\n\u003cli\u003eAppendices\u003c\/li\u003e\n\u003cli\u003eUpper and lower limits\u003c\/li\u003e\n\u003cli\u003eCaratheodory's approach to measure theory\u003c\/li\u003e\n\u003cli\u003eAcknowledgments\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex of symbols\u003c\/li\u003e\n\u003cli\u003eAuthor index\u003c\/li\u003e\n\u003cli\u003eSubject index\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52589078610200,"sku":"9781470476236","price":91.99,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-invitation-to-fractal-geometry-fractal-dimensions-self-similarity-and-fractal-curves-hardback-9781470476236","provider":"Freshly Printed Books","version":"1.0","type":"link"}