Abstract
We present here a class of positive operator semigroups that arise in studying dynamical systems. The main idea is to linearize a given (nonlinear) system by considering another state space. The linear operator which acts on this new space is called the Koopman operator. It is named after B. O. Koopman, who used this in the 1930s together with G. D. Birkhoff and J. von Neumann to prove the so-called ergodic theorems.
Access provided by CONRICYT-eBooks. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Invariant Measure
- Banach Lattice
- Continuous Semigroup
- Invariant Probability Measure
- Contraction Semigroup
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Bátkai, A., Fijavž, M.K., Rhandi, A. (2017). Koopman Semigroups. In: Positive Operator Semigroups. Operator Theory: Advances and Applications, vol 257. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42813-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-42813-0_16
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-42811-6
Online ISBN: 978-3-319-42813-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)