A note on Kowalevski exponents and the non-existence of an additional analytic integral
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Publication:3830591
DOI10.1007/BF01234270zbMath0675.70018MaRDI QIDQ3830591
Publication date: 1989
Published in: Celestial Mechanics (Search for Journal in Brave)
two degrees of freedomHamiltonian systemshomogeneous rational potentialimaginary Kowalevski exponentsnon-existence of an additional analytic integralnon-integrability of the system
Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items (10)
On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n ⋮ On non-integrability of general systems of differential equations ⋮ On the polynomial integrability of the Hoyer systems ⋮ Darboux polynomials, balances and Painlevé property ⋮ Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3 ⋮ Nonintegrability of Bianchi VIII Hamiltonian system ⋮ Necessary conditions for the existence of particular algebraic first integrals ⋮ Numerical evidence of nonintegrability of certain Lie-Poisson system
Cites Work
- Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
- Non-integrability of Hénon-Heiles system and a theorem of Ziglin
- A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
- Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems
- Non-integrability of the truncated Toda lattice Hamiltonian at any order
- Algebraic geometrical methods in Hamiltonian mechanics
- Necessary condition for the existence of algebraic first integrals
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