# Examples of complete solvability of 2D classical superintegrable systems

@article{Chen2015ExamplesOC, title={Examples of complete solvability of 2D classical superintegrable systems}, author={Yuxuan Chen and Ernest G. Kalnins and Qiushi Li and Willard Miller}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2015}, volume={11}, pages={088} }

Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved algebraically. In this paper we show explicitly, mostly through examples of 2nd order superintegrable systems in 2 dimensions, how the trajectories can be determined in detail using rather elementary algebraic, geometric and analytic methods applied to the closed…

## 4 Citations

### Global structure and geodesics for Koenigs superintegrable systems

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We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their…

### Global structure and geodesics for Koenigs superintegrable systems

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We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their…

### From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry

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### Elliptic curve arithmetic and superintegrable systems

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The harmonic oscillator and the Kepler problem are superintegrable systems which admit more integrals of motion than degrees of freedom and all these integrals are polynomials in momenta. We present…

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