An invitation to fractal geometry : fractal dimensions, self-similarity and fractal curves /

Gespeichert in:
Weitere Titel:
Introduction to concepts in fractal geometry
Metric spaces and fixed point theorem
Measure theory and integrals
Iterated function systems and self-similarity
Introduction to Hausdorff measure and dimension
$\delta $-Approximate Hausdorff measures, via Carathéodory's theory
Construction and properties of Hausdorff measure
Minkowski content and Minkowski dimension
Epilogue: A primer of fractal curves and their complex dimensions
Upper and lower limits
Carathéodory's approach to measure theory
Hauptverfasser:
Lapidus, Michel L., Radunović, Goran
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
Providence, Rhode Island : American Mathematical Society, [2024]
Umfang:
1 online resource (pages cm.)
Mode of access : World Wide Web
Format Details:
Mode of access : World Wide Web
Bibliografie:
Includes bibliographical references and index.
Schriftenreihe:
Graduate Studies in Mathematics,
Sekundärform:
Publikations­art: Electronic reproduction.
Verlag: Providence, Rhode Island :: American Mathematical Society.
Publikations­datum: 2024
ISBN:
9781470478964 (online)
ISSN:
1065-7339
DOI:
10.1090/gsm/247
Zugangseinschränkungen:
Access is restricted to licensed institutions
Schlagworte:
Fractals.
Number theory > Zeta and $L$-functions: analytic theory > Other Dirichlet series and zeta functions.
Measure and integration > Classical measure theory > Contents, measures, outer measures, capacities.
Measure and integration > Classical measure theory > Length, area, volume, other geometric measure theory.
Measure and integration > Classical measure theory > Fractals.
Measure and integration > Set functions, measures and integrals with values in abstract spaces > Set functions, measures and integrals with values in ordered spaces.
Functions of a complex variable > Entire and meromorphic functions, and related topics > Representations of entire functions by series and integrals.
Partial differential equations > Spectral theory and eigenvalue problems > Asymptotic distribution of eigenvalues and eigenfunctions.
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables > Singular and oscillatory integrals (Calderón-Zygmund, etc.).
Integral transforms, operational calculus > Integral transforms, operational calculus > General transforms.
Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Boundary value problems on manifolds.
Number theory > Zeta and $L$-functions: analytic theory > $\zeta (s)$ and $L(s, \chi)$.
Functions of a complex variable > Entire and meromorphic functions, and related topics > Meromorphic functions, general theory.
Dynamical systems and ergodic theory > Smooth dynamical systems: general theory > Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
Dynamical systems and ergodic theory > Smooth dynamical systems: general theory > Dimension theory of dynamical systems.
Sequences, series, summability > Convergence and divergence of infinite limiting processes > Convergence and divergence of integrals.
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables > Function spaces arising in harmonic analysis.
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables > Harmonic analysis and PDE.
Integral transforms, operational calculus > Integral transforms, operational calculus > Laplace transform.
Integral equations > Inverse problems > Inverse problems.
Quantum theory > General mathematical topics and methods in quantum theory > Semiclassical techniques, including WKB and Maslov methods.
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