Abstract
We introduce an operator calculus that will allow us to work with nonlinear systems and flows as with linear ones, at least at the formal level. The idea is to replace a nonlinear object, a smooth manifold M,by a linear, although infinite-dimensional one: the commutative algebra of smooth functions on M (for details, see [19], [22]). For basic definitions and facts of functional analysis used in this chapter, one can consult e.g. [144].
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 Berlin Heidelberg
About this chapter
Cite this chapter
Agrachev, A.A., Sachkov, Y.L. (2004). Elements of Chronological Calculus. In: Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06404-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-06404-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05907-0
Online ISBN: 978-3-662-06404-7
eBook Packages: Springer Book Archive