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Comment on ,,On the integrability of 2D Hamiltonian systems with variable Gaussian curvature” by A. A. Elmandouh by Wojciech Szumiński; Andrzej J. Maciejewski is a Engineering article available to read on EtoBox.

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## Abstract In the paper [1], the author formulates in Theorem 2 necessary conditions for integrability of a certain class of Hamiltonian systems with non-constant Gaussian curvature, which depends on local coordinates. We give a counterexample to show that this theorem is not correct in general. This contradiction is explained in some extent. However, the main result of this note is our theorem that gives new simple and easy to check necessary conditions to integrability of the system considered in [1]. We present several examples, which show that the obtained conditions are effective. Moreover, we justify that our criterion can be extended to wider class of systems, which are given by non-meromorphic Hamiltonian functions.

Who reads Comment on ,,On the integrability of 2D Hamiltonian systems with variable Gaussian curvature” by A. A. Elmandouh?

Author

Wojciech Szumiński; Andrzej J. Maciejewski

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Engineering (Physical Sciences)