Abstract
© 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.
Original language | English |
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Article number | 1750045 |
Journal | Communications in Contemporary Mathematics |
Volume | 20 |
DOIs | |
Publication status | Published - 1 Dec 2018 |
Keywords
- Darboux first integrals
- Darboux polynomials
- Hamiltonian systems
- exponential factors
- polynomial integrability
- weight-homogenous differential systems