All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
From MaRDI portal
Publication:2476389
DOI10.1016/j.physleta.2004.05.042zbMath1138.37325OpenAlexW2079376884WikidataQ104404979 ScholiaQ104404979MaRDI QIDQ2476389
Maria Przybylska, Andrzej J. Maciejewski
Publication date: 19 March 2008
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physleta.2004.05.042
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)
Related Items
Polynomial integrability of Hamiltonian systems with homogeneous potentials of degree \(k\) ⋮ ON A POLYTOPE CONTAINING ALL COMPACT INVARIANT SETS FOR A CLASS OF NATURAL POLYNOMIAL HAMILTONIAN SYSTEMS ⋮ DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY ⋮ On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n ⋮ Non-integrability of Hénon-Heiles system ⋮ Integrable deformations of integrable Hamiltonian systems ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Darboux and analytic integrability of five‐dimensional semiclassical Jaynes–Cummings system ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ On the integrability of the Hamiltonian systems with homogeneous polynomial potentials ⋮ Darboux points and integrability analysis of Hamiltonian systems with homogeneous rational potentials ⋮ Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree - 2 ⋮ Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom ⋮ Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nongeneric cases ⋮ Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree --3 ⋮ Differential Galois obstructions for integrability of homogeneous Newton equations ⋮ Weak-Painlevé property and integrability of general dynamical systems ⋮ Dynamics of mechanical systems with polynomial potentials ⋮ On the integrability of a system describing the stationary solutions in Bose-Fermi mixtures ⋮ Integrable planar homogeneous potentials of degree \(- 1\) with small eigenvalues ⋮ Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3 ⋮ Integrability conditions of geodesic flow on homogeneous Monge manifolds ⋮ Finiteness of integrable \(n\)-dimensional homogeneous polynomial potentials ⋮ Dynamics and periodic solutions in cubic polynomial Hamiltonian systems ⋮ On algebraic construction of certain integrable and super-integrable systems ⋮ Non-integrability of the anisotropic Stormer problem and the isosceles three-body problem ⋮ Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree \(-4\) ⋮ Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4 ⋮ Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential ⋮ Third order integrability conditions for homogeneous potentials of degree −1
Cites Work
- Unnamed Item
- Unnamed Item
- Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
- A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
- On algebraic solutions of Lame's differential equation
- Galoisian obstructions to integrability of Hamiltonian systems. I.
- A new necessary condition for the integrability of Hamiltonian systems with a two-dimensional homogeneous potential
- Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
- A list of all integrable two-dimensional homogeneous polynomial potentials with a polynomial integral of order at most four in the momenta
- Differential Galois theory and non-integrability of Hamiltonian systems
- Kovalevskaya, Lyapunov, Painlevé, Ziglin and the differential Galois theory