Fractal-Based Methods in Analysis

• Main Authors: Kunze, Herb (Author), La Torre, Davide (Author), Mendivil, Franklin (Author), Vrscay, Edward R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2012.
• Subjects: Mathematics.; Approximation theory.; Dynamics.; Ergodic theory.; Differential equations.; Mathematical models.; Physics.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.; Approximations and Expansions.; Mathematical Modeling and Industrial Mathematics.; Ordinary Differential Equations.

The idea of modeling the behavior of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional...

Table of Contents:

• What do we mean by “Fractal-Based Analysis"
• Basic IFS
• IFS on Spaces of Functions
• IFS, Multifunctions, and Measure-Valued Functions. -IFS on Spaces of Measures.-The Chaos Game.-Inverse Problems and Fractal-Based Methods.-Further Developments and Extensions
• References
• Index.