Abstract
A well-known theorem states that if a level surface of a Hamiltonian is convex, then it contains a periodic trajectory of the Hamiltonian system [142], [147]. In this chapter we prove a more general statement as an application of optimal control theory for linear systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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). Hamiltonian Systems with Convex Hamiltonians. 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_14
Download citation
DOI: https://doi.org/10.1007/978-3-662-06404-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05907-0
Online ISBN: 978-3-662-06404-7
eBook Packages: Springer Book Archive