TY - CHAP
T1 - A Review of Multiple-Time-Scale Dynamics
T2 - Fundamental Phenomena and Mathematical Methods
AU - Kristiansen, Kristian Uldall
PY - 2023
Y1 - 2023
N2 - In this chapter, we review the most fundamental phenomena in differentiable, finite-dimensional multiple-time scale systems as well as the geometric singular perturbation theory (GSPT) that can be used to analyze such systems. We put special emphasis on loss of normal hyperbolicity and illustrate how it relates to the different phenomena. Moreover, by working on lower-dimensional model problems, we review the main technical tool of GSPT, the blowup method, and demonstrate - in line with recent research in this area - how it may provide detailed insight into problems of this kind.
AB - In this chapter, we review the most fundamental phenomena in differentiable, finite-dimensional multiple-time scale systems as well as the geometric singular perturbation theory (GSPT) that can be used to analyze such systems. We put special emphasis on loss of normal hyperbolicity and illustrate how it relates to the different phenomena. Moreover, by working on lower-dimensional model problems, we review the main technical tool of GSPT, the blowup method, and demonstrate - in line with recent research in this area - how it may provide detailed insight into problems of this kind.
U2 - 10.1007/16618_2023_75
DO - 10.1007/16618_2023_75
M3 - Book chapter
T3 - Mathematics Online First Collections
SP - 1
EP - 55
BT - Mathematics Online First Collections
PB - Springer
ER -