References
- [Diacu et al. 12] F. Diacu, E. Perez-Chavela, and M. Santoprete. “The n-body Problem in Spaces of Constant Curvature. Part I: Relative Equilibria,” J. Nonlinear Sci. 22 (2012), 247–266.
- [Dods 17] V. Dods. “Kepler–Heisenberg Problem Computational Tool Suite.” Available at (https://github.com/vdods/heisenberg), 2017.
- [Fiorani et al. 03] E. Fiorani, G. Giachetta, and G. Sardanashvily. “The Liouville–Arnold–Nekhoroshev Theorem for Non-Compact Invariant Manifolds,” J. Phys. A 36 (2003), L101–L107.
- [Folland 73] G. Folland. “A Fundamental Solution to a Subelliptic Operator,” Bull. Amer. Math. Soc. 79 (1973), 373–376.
- [Katok and Hasselblatt 95] A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press (1995).
- [Montgomery 02] R. Montgomery. A Tour of Subriemannian Geometries, Their Geodesics and Applications, AMS Mathematical Surveys and Monographs91 (2002).
- [Montgomery and Shanbrom 15] R. Montgomery and C. Shanbrom. “Keplerian Motion on the Heisenberg Group and Elsewhere, Geometry, Mechanics, and Dynamics: The Legacy of Jerry Marsden,” Fields Inst. Comm. 73 (2015), 319–342.
- [Nauenberg 01] M. Nauenberg. “Periodic Orbits for Three Particles with Finite Angular Momentum,” Phys. Lett. A 292 (2001), 93–99.
- [Nauenberg 07] M. Nauenberg. “Continuity and Stability of Families of Figure Eight Orbits with Finite Angular Momentum,” Celestial Mech. Dynam. Astronom. 97 (2007), 1–15.
- [Pihajoki 15] P. Pihajoki. “Explicit Methods in Extended Phase Space for Inseparable Hamiltonian Problems,” Celestial Mech. Dynam. Astronom. 121 (2015), 211–231.
- [Shanbrom 14] C. Shanbrom. “Periodic Orbits in the Kepler–Heisenberg Problem,” J. Geom. Mech. 6 (2014), 261–278.
- [Tabachnikov 05] S. Tabachnikov. Geometry and Billiards, AMS Student Mathematical Library 30 (2005).
- [Tao 16] M. Tao. “Explicit Symplectic Approximation of Nonseparable Hamiltonians: Algorithm and Long Time Performance,” Phys. Rev. E 94 (2016), 043303.