Advertisement

Polynomial Integrals of Hamiltonian Systems

Chapter
  • 323 Downloads
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 31)

Abstract

In this chapter we present specific methods of searching for Hamiltonian systems which admit first integrals polynomial in momenta. This problem is actual because in Hamiltonian mechanics the majority of known integrals are either polynomials in momenta or functions of these polynomials (see §1 of Chap. II). The problem of the existence of linear and quadratic integrals is quite elementary. Usually, it can be easily solved. For integrals whose degree is not fixed in advance, however it is much more difficult. At present, it is solved only for some classes of Hamiltonian systems.

Keywords

Hamiltonian System Trigonometric Polynomial Hamiltonian Function Dynkin Diagram Toda Lattice 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations