|
Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Rational Integrability of Trigonometric Polynomial Potentials on the Flat Torus
Thierry Combot Scuola Normale Superiore, Centro di Ricerca Matematica Ennio De Giorgi, Laboratorio Fibonacci, Piazza Cavalieri, 56127 Pisa
Аннотация:
We consider a lattice $\mathcal{L}\subset \mathbb{R}^n$ and a trigonometric potential $V$ with frequencies
$k\in\mathcal{L}$. We then prove a strong rational integrability condition on $V$, using the support of its Fourier transform.
We then use this condition to prove that a real trigonometric polynomial potential is rationally integrable if and only if it
separates up to rotation of the coordinates. Removing the real condition, we also make a classification of rationally integrable
potentials in dimensions $2$ and $3$ and recover several integrable cases. After a complex change of variables, these potentials
become real and correspond to generalized Toda integrable potentials. Moreover, along the proof, some of them with high-degree
first integrals are explicitly integrated.
Ключевые слова:
trigonometric polynomials, differential Galois theory, integrability, Toda lattice.
Поступила в редакцию: 27.04.2017 Принята в печать: 01.06.2017
Образец цитирования:
Thierry Combot, “Rational Integrability of Trigonometric Polynomial Potentials on the Flat Torus”, Regul. Chaotic Dyn., 22:4 (2017), 386–497
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd262 https://www.mathnet.ru/rus/rcd/v22/i4/p386
|
|