Polynomial Integrals of Hamiltonian Systems
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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.
KeywordsHamiltonian System Trigonometric Polynomial Hamiltonian Function Dynkin Diagram Toda Lattice
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