LEADER 05851nam 2200673 450 001 9910453807903321 005 20210812135123.0 010 $a1-118-76286-X 010 $a1-118-76285-1 035 $a(UkCvUL)(CKB)2550000001159897 035 $a(UkCvUL)(EBL)1557285 035 $a(UkCvUL)(OCoLC)863823803 035 $a(UkCvUL)(SSID)ssj0001040604 035 $a(UkCvUL)(PQKBManifestationID)11595580 035 $a(UkCvUL)(PQKBTitleCode)TC0001040604 035 $a(UkCvUL)(PQKBWorkID)11001929 035 $a(UkCvUL)(PQKB)11526873 035 $a(UkCvUL)(MiAaPQ)EBC1557285 035 $a(UkCvUL)(DLC) 2013031708 035 $a(UkCvUL)(Au-PeEL)EBL1557285 035 $a(UkCvUL)(CaPaEBR)ebr10804648 035 $a(UkCvUL)(CaONFJC)MIL543102 035 $a(UkCvUL)992550000001159897 035 $a(EXLCZ)992550000001159897 100 $a20130802d2014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractal geometry $emathematical foundations and applications /$fKenneth Falconer 205 $aThird edition. 210 1$aHoboken :$cJohn Wiley & Sons,$d2014. 215 $a1 online resource (400 p.) 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references and index. 327 $aCover; 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 references 327 $aExercisesChapter 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; Exercises 327 $aChapter 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; Exercises 327 $aPart 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 graphs 327 $a11.2 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; Exercises 327 $aChapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set 330 $a"This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science. New research developments are highlighted, such as porosity, while covering other much more sophisticated topics, such as fractal aspects of conformal invariance, complex dimensions, and non-commutative fractal geometry. The book emphasizes dimension in its various forms, but other notions of fractality are also prominent"--$cProvided by publisher. 330 $a"This comprehensive, accessible and very popular textbook presents fractal geometry at a level accessible to a final year undergraduate mathematician or physicist whilst also providing a useful primer or reference for the research mathematician or scientist"--$cProvided by publisher. 606 $aFractals 606 $aDimension theory (Topology) 608 $aElectronic books. 615 0$aFractals. 615 0$aDimension theory (Topology) 676 $a514/.742 686 $aMAT031000$2bisacsh 700 $aFalconer$b K. 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