Geodesics on the ellipsoid and monodromy
From MaRDI portal
Publication:2475444
DOI10.1016/j.geomphys.2007.07.006zbMath1148.53026arXivmath-ph/0609073OpenAlexW1966670646MaRDI QIDQ2475444
Chris M. Davison, Holger R. Dullin, Alexei V. Bolsinov
Publication date: 11 March 2008
Published in: Journal of Geometry and Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0609073
Geodesics in global differential geometry (53C22) Momentum maps; symplectic reduction (53D20) Constrained dynamics, Dirac's theory of constraints (70H45) Geodesic flows in symplectic geometry and contact geometry (53D25)
Related Items
Geodesics on Ellipsoids ⋮ Uncovering fractional monodromy ⋮ The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards ⋮ The degenerate C. Neumann system. I: Symmetry reduction and convexity ⋮ Integrable systems on a sphere, an ellipsoid and a hyperboloid ⋮ Geodesic flow on an intersection of several confocal quadrics in $\mathbb{R}^n$ ⋮ Regular and irregular geodesics on spherical harmonic surfaces ⋮ Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$ ⋮ The conjugate locus in convex 3-manifolds ⋮ Topological atlas of the Kovalevskaya top in a double field ⋮ Geodesic flow on three-dimensional ellipsoids with equal semi-axes ⋮ Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere ⋮ The Picard–Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system ⋮ The number of connected components in the preimage of a regular value of the momentum mapping for the geodesic flow on ellipsoid
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geodesics on the ellipsoid
- A note on focus-focus singularities
- Monodromy in the resonant swing spring
- Monodromy in the hydrogen atom in crossed fields
- Quantum monodromy in prolate ellipsoidal billiards
- Separable systems of Stäckel
- The problem of two fixed centers: bifurcations, actions, monodromy
- Singularities of integrable geodesic flows on multidimensional torus and sphere
- Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics
- Monodromy, diabolic points, and angular momentum coupling
- On global action-angle coordinates
- Geodesics on quadrics and a mechanical problem of C. Neumann.
- Integrable Hamiltonian system with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle type
- Maslov indices and monodromy
- Actions of the Neumann systems via Picard-Fuchs equations
