Abstract
This is perhaps the most challenging chapter of this book in that we attempt to show how homology can be used in nonlinear analysis and dynamical systems. As mentioned in the Preface, algebraic topology was developed to solve problems in these subjects. Thus, on one hand, some of the material (most notably Sections 10.4 and 10.5) is classical and has a rich history. On the other hand, the focus of Section 10.6, combining numerical analysis with homology via the computer to obtain mathematically rigorous results, is a cutting-edge topic. We assume that the background and interest of our readers are equally varied, ranging from an individual with no background in dynamics hoping to learn the mathematical theory to others whose primary goal is to understand how to apply these ideas to specific nonlinear systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Nonlinear Dynamics. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_10
Download citation
DOI: https://doi.org/10.1007/0-387-21597-2_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2354-7
Online ISBN: 978-0-387-21597-6
eBook Packages: Springer Book Archive