05851nam 2200673 450 991045380790332120210812135123.01-118-76286-X1-118-76285-1(UkCvUL)(CKB)2550000001159897(UkCvUL)(EBL)1557285(UkCvUL)(OCoLC)863823803(UkCvUL)(SSID)ssj0001040604(UkCvUL)(PQKBManifestationID)11595580(UkCvUL)(PQKBTitleCode)TC0001040604(UkCvUL)(PQKBWorkID)11001929(UkCvUL)(PQKB)11526873(UkCvUL)(MiAaPQ)EBC1557285(UkCvUL)(DLC) 2013031708(UkCvUL)(Au-PeEL)EBL1557285(UkCvUL)(CaPaEBR)ebr10804648(UkCvUL)(CaONFJC)MIL543102(UkCvUL)992550000001159897(EXLCZ)99255000000115989720130802d2014 uy 0engur|n|---|||||txtccrFractal geometry mathematical foundations and applications /Kenneth FalconerThird edition.Hoboken :John Wiley & Sons,2014.1 online resource (400 p.)Description based upon print version of record.Includes bibliographical references and index.Cover; Title Page; Copyright; Contents; Preface to the first edition; Preface to the second edition; Preface to the third edition; Course suggestions; Introduction; Part I Foundations; Chapter 1 Mathematical background; 1.1 Basic set theory; 1.2 Functions and limits; 1.3 Measures and mass distributions; 1.4 Notes on probability theory; 1.5 Notes and references; Exercises; Chapter 2 Box-counting dimension; 2.1 Box-counting dimensions; 2.2 Properties and problems of box-counting dimension; 2.3 Modified box-counting dimensions; 2.4 Some other definitions of dimension; 2.5 Notes and referencesExercisesChapter 3 Hausdorff and packing measures and dimensions; 3.1 Hausdorff measure; 3.2 Hausdorff dimension; 3.3 Calculation of Hausdorff dimension-simple examples; 3.4 Equivalent definitions of Hausdorff dimension; 3.5 Packing measure and dimensions; 3.6 Finer definitions of dimension; 3.7 Dimension prints; 3.8 Porosity; 3.9 Notes and references; Exercises; Chapter 4 Techniques for calculating dimensions; 4.1 Basic methods; 4.2 Subsets of finite measure; 4.3 Potential theoretic methods; 4.4 Fourier transform methods; 4.5 Notes and references; ExercisesChapter 5 Local structure of fractals5.1 Densities; 5.2 Structure of 1-sets; 5.3 Tangents to s-sets; 5.4 Notes and references; Exercises; Chapter 6 Projections of fractals; 6.1 Projections of arbitrary sets; 6.2 Projections of s-sets of integral dimension; 6.3 Projections of arbitrary sets of integral dimension; 6.4 Notes and references; Exercises; Chapter 7 Products of fractals; 7.1 Product formulae; 7.2 Notes and references; Exercises; Chapter 8 Intersections of fractals; 8.1 Intersection formulae for fractals; 8.2 Sets with large intersection; 8.3 Notes and references; ExercisesPart II Applications and ExamplesChapter 9 Iterated function systems-self-similar and self-affine sets; 9.1 Iterated function systems; 9.2 Dimensions of self-similar sets; 9.3 Some variations; 9.4 Self-affine sets; 9.5 Applications to encoding images; 9.6 Zeta functions and complex dimensions; 9.7 Notes and references; Exercises; Chapter 10 Examples from number theory; 10.1 Distribution of digits of numbers; 10.2 Continued fractions; 10.3 Diophantine approximation; 10.4 Notes and references; Exercises; Chapter 11 Graphs of functions; 11.1 Dimensions of graphs11.2 Autocorrelation of fractal functions11.3 Notes and references; Exercises; Chapter 12 Examples from pure mathematics; 12.1 Duality and the Kakeya problem; 12.2 Vitushkin's conjecture; 12.3 Convex functions; 12.4 Fractal groups and rings; 12.5 Notes and references; Exercises; Chapter 13 Dynamical systems; 13.1 Repellers and iterated function systems; 13.2 The logistic map; 13.3 Stretching and folding transformations; 13.4 The solenoid; 13.5 Continuous dynamical systems; 13.6 Small divisor theory; 13.7 Lyapunov exponents and entropies; 13.8 Notes and references; ExercisesChapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set"This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science. New research developments are highlighted, such as porosity, while covering other much more sophisticated topics, such as fractal aspects of conformal invariance, complex dimensions, and non-commutative fractal geometry. The book emphasizes dimension in its various forms, but other notions of fractality are also prominent"--Provided by publisher."This comprehensive, accessible and very popular textbook presents fractal geometry at a level accessible to a final year undergraduate mathematician or physicist whilst also providing a useful primer or reference for the research mathematician or scientist"--Provided by publisher.FractalsDimension theory (Topology)Electronic books.Fractals.Dimension theory (Topology)514/.742MAT031000bisacshFalconer K. J.1952-21298MiAaPQMiAaPQMiAaPQBOOK9910453807903321Fractal geometry79526UNINA