# Factorization approach to superintegrable systems: Formalism and applications

## Abstract

The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic oscillator on the Euclidean plane is reviewed, and new classical (super) integrable anisotropic oscillators on the sphere are constructed. The Tremblay–Turbiner–Winternitz system on the Euclidean plane is also studied from this viewpoint.

- Authors:

- Universidad de Burgos, Departamento de Física (Spain)
- Ankara University, Department of Physics, Faculty of Science (Turkey)
- Universidad de Valladolid, Departamento de Física Teórica, Atómica y Óptica (Spain)

- Publication Date:

- OSTI Identifier:
- 22613974

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 80; Journal Issue: 2; Other Information: Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ANISOTROPY; EUCLIDEAN SPACE; FACTORIZATION; HAMILTONIANS; INTEGRAL CALCULUS; OSCILLATORS

### Citation Formats

```
Ballesteros, Á., E-mail: angelb@ubu.es, Herranz, F. J., E-mail: fjherranz@ubu.es, Kuru, Ş., E-mail: kuru@science.ankara.edu.tr, and Negro, J., E-mail: jnegro@fta.uva.es.
```*Factorization approach to superintegrable systems: Formalism and applications*. United States: N. p., 2017.
Web. doi:10.1134/S1063778817020053.

```
Ballesteros, Á., E-mail: angelb@ubu.es, Herranz, F. J., E-mail: fjherranz@ubu.es, Kuru, Ş., E-mail: kuru@science.ankara.edu.tr, & Negro, J., E-mail: jnegro@fta.uva.es.
```*Factorization approach to superintegrable systems: Formalism and applications*. United States. doi:10.1134/S1063778817020053.

```
Ballesteros, Á., E-mail: angelb@ubu.es, Herranz, F. J., E-mail: fjherranz@ubu.es, Kuru, Ş., E-mail: kuru@science.ankara.edu.tr, and Negro, J., E-mail: jnegro@fta.uva.es. Wed .
"Factorization approach to superintegrable systems: Formalism and applications". United States.
doi:10.1134/S1063778817020053.
```

```
@article{osti_22613974,
```

title = {Factorization approach to superintegrable systems: Formalism and applications},

author = {Ballesteros, Á., E-mail: angelb@ubu.es and Herranz, F. J., E-mail: fjherranz@ubu.es and Kuru, Ş., E-mail: kuru@science.ankara.edu.tr and Negro, J., E-mail: jnegro@fta.uva.es},

abstractNote = {The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic oscillator on the Euclidean plane is reviewed, and new classical (super) integrable anisotropic oscillators on the sphere are constructed. The Tremblay–Turbiner–Winternitz system on the Euclidean plane is also studied from this viewpoint.},

doi = {10.1134/S1063778817020053},

journal = {Physics of Atomic Nuclei},

number = 2,

volume = 80,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}

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