Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics

Dorin Dutkay; Palle Jorgensen

doi:10.1007/3-7643-7588-4_4

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Book chapter

Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics

Dorin Dutkay and Palle Jorgensen

Wavelets, Multiscale Systems and Hypercomplex Analysis, pp.87-126

Operator Theory: Advances and Applications, Birkhäuser Basel

2006

DOI: 10.1007/3-7643-7588-4_4

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Abstract

We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to nonlinear dynamics.The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as the discrete systems built on rational functions of one complex variable and the corresponding Julia sets, and state spaces of subshifts in symbolic dynamics. Our paper serves to motivate and survey our recent results in this general area. Hence we leave out some proofs, but instead add a number of intuitive ideas which we hope will make the subject more accessible to researchers in operator theory and systems theory.

Abstract Harmonic Analysis

Operator Theory

Systems Theory, Control

Functions of a Complex Variable

Analysis

Mathematics

Details

Title: Subtitle: Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics
Creators: Dorin Dutkay - Rutgers University
Palle Jorgensen - The University of Iowa
Contributors: Daniel Alpay (Editor)
Annemarie Luger (Editor)
Harald Woracek (Editor)
Resource Type: Book chapter
Publication Details: Wavelets, Multiscale Systems and Hypercomplex Analysis, pp.87-126
Series: Operator Theory: Advances and Applications
DOI: 10.1007/3-7643-7588-4_4
Publisher: Birkhäuser Basel; Basel
Language: English
Date published: 2006
Academic Unit: Mathematics
Record Identifier: 9983985704002771

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