Overview of the differential Galois integrability conditions for non-homogeneous potentials

Andrzej J. Maciejewski; Maria Przybylska

Banach Center Publications (2011)

  • Volume: 94, Issue: 1, page 221-232
  • ISSN: 0137-6934

Abstract

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We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form H = 1 / 2 ∑ i = 1 n p ² i + V ( q ) , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form V = V k + V K , where V k and V K are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable systems which were obtained by applying our main theorem.

How to cite

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Andrzej J. Maciejewski, and Maria Przybylska. "Overview of the differential Galois integrability conditions for non-homogeneous potentials." Banach Center Publications 94.1 (2011): 221-232. <http://eudml.org/doc/282183>.

@article{AndrzejJ2011,
abstract = {We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form $H = 1/2 ∑_\{i=1\}^\{n\} p²_\{i\} + V(q)$, where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form $V = V_k + V_K$, where $V_k$ and $V_K$ are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable systems which were obtained by applying our main theorem.},
author = {Andrzej J. Maciejewski, Maria Przybylska},
journal = {Banach Center Publications},
keywords = {differential Galois theory; Hamiltonian systems; integrability; Morales-Ramis theory; non-integrability},
language = {eng},
number = {1},
pages = {221-232},
title = {Overview of the differential Galois integrability conditions for non-homogeneous potentials},
url = {http://eudml.org/doc/282183},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Andrzej J. Maciejewski
AU - Maria Przybylska
TI - Overview of the differential Galois integrability conditions for non-homogeneous potentials
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 221
EP - 232
AB - We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form $H = 1/2 ∑_{i=1}^{n} p²_{i} + V(q)$, where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form $V = V_k + V_K$, where $V_k$ and $V_K$ are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable systems which were obtained by applying our main theorem.
LA - eng
KW - differential Galois theory; Hamiltonian systems; integrability; Morales-Ramis theory; non-integrability
UR - http://eudml.org/doc/282183
ER -

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