Non-integrability of the Kepler and the two-body problems on the Heisenberg group
DOI10.3842/SIGMA.2021.074zbMath1489.37073arXiv2103.10495MaRDI QIDQ2236615
Tomasz Stachowiak, Andrzej J. Maciejewski
Publication date: 25 October 2021
Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.10495
Heisenberg groupintegrabilitytwo-body problemKepler problemdifferential Galois groupsub-Riemannian manifoldMorales-Ramis theory
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Two-body problems (70F05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Dynamical systems in classical and celestial mechanics (37N05) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Abstract differential equations (12H20) Sub-Riemannian geometry (53C17) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)
Cites Work
- Unnamed Item
- An algorithm for solving second order linear homogeneous differential equations
- Kovacic's algorithm and its application to some families of special functions
- Necessary conditions for Liouvillian solutions of (third order) linear differential equations
- Galoisian obstructions to integrability of Hamiltonian systems. I.
- Integrability of Hamiltonian systems with algebraic potentials
- Absolute reducibility of differential operators and Galois groups
- Self-similarity in the Kepler-Heisenberg problem
- Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
- Periodic orbits in the Kepler-Heisenberg problem
- The spatial problem of 2 bodies on a sphere. Reduction and stochasticity
- Keplerian Dynamics on the Heisenberg Group and Elsewhere
- Galois groups and elementary solutions of some linear differential equations.
- A fundamental solution for a subelliptic operator
