Abstract
A common feature of the various approaches to the problem of integration of Hamiltonian systems indicated in Chapter 4 is the existence of a sufficiently large number of independent first integrals, or “conservation laws”. Unfortunately, in typical situations, not only do we fail to find such integrals, but they simply do not exist, since the trajectories of Hamiltonian systems, generally speaking, do not lie on low-dimensional invariant manifolds. We have in mind, of course, integrals which exist on the entire phase space: a complete set of independent first integrals always exists in a small neighborhood of a nonsingular point.
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
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Arnold, V.I. (1988). Nonintegrable Systems. In: Arnold, V.I. (eds) Dynamical Systems III. Encyclopaedia of Mathematical Sciences, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02535-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-02535-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02537-6
Online ISBN: 978-3-662-02535-2
eBook Packages: Springer Book Archive