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TMF, 2016, Volume 186, Number 3, Pages 443–455 (Mi tmf8948)  

Two integrable systems with integrals of motion of degree four

A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We discuss the possibility of using second-order Killing tensors to construct Liouville-integrable Hamiltonian systems that are not Nijenhuis integrable. As an example, we consider two Killing tensors with a nonzero Haantjes torsion that satisfy weaker geometric conditions and also three-dimensional systems corresponding to them that are integrable in Euclidean space and have two quadratic integrals of motion and one fourth-order integral in momenta.

Keywords: Hamilton–Jacobi equation, separation of variables, Killing tensor

Funding Agency Grant Number
Russian Science Foundation 15-11-30007
This work was supported by the Russian Science Foundation under grant 15-11-30007.


DOI: https://doi.org/10.4213/tmf8948

Full text: PDF file (384 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 186:3, 383–394

Bibliographic databases:

PACS: 02.30.Ik; 02.40.Ky
MSC: 70H06, 53B21
Received: 13.04.2015

Citation: A. V. Tsiganov, “Two integrable systems with integrals of motion of degree four”, TMF, 186:3 (2016), 443–455; Theoret. and Math. Phys., 186:3 (2016), 383–394

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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