Standard

Unique resonant normal forms for area-preserving maps at an elliptic fixed point. / Gelfreich, Vassili; Gelfreikh, Natalia.

в: Nonlinearity, Том 22, № 4, 24.07.2009, стр. 783-810.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Gelfreich, V & Gelfreikh, N 2009, 'Unique resonant normal forms for area-preserving maps at an elliptic fixed point', Nonlinearity, Том. 22, № 4, стр. 783-810. https://doi.org/10.1088/0951-7715/22/4/006

APA

Gelfreich, V., & Gelfreikh, N. (2009). Unique resonant normal forms for area-preserving maps at an elliptic fixed point. Nonlinearity, 22(4), 783-810. https://doi.org/10.1088/0951-7715/22/4/006

Vancouver

Gelfreich V, Gelfreikh N. Unique resonant normal forms for area-preserving maps at an elliptic fixed point. Nonlinearity. 2009 Июль 24;22(4):783-810. https://doi.org/10.1088/0951-7715/22/4/006

Author

Gelfreich, Vassili ; Gelfreikh, Natalia. / Unique resonant normal forms for area-preserving maps at an elliptic fixed point. в: Nonlinearity. 2009 ; Том 22, № 4. стр. 783-810.

BibTeX

@article{022ff5f78d9743668f7899829257415d,
title = "Unique resonant normal forms for area-preserving maps at an elliptic fixed point",
abstract = "We study possible simplifications of normal forms for area-preserving maps near a resonant elliptic fixed point. In the generic case we prove that at all orders the Takens normal form vector field can be transformed to the particularly simple form described by the formal interpolating Hamiltonian The form of formal series A and B depends on the order of the resonance n. For each n ≥ 3 we establish which terms of the series can be eliminated by a canonical substitution and derive a unique normal form which provides a full set of formal invariants with respect to canonical changes in coordinates. We extend these results to families of area-preserving maps. Then the formal interpolating Hamiltonian takes a form similar to the case of an individual map but involves formal power series in action I and the parameter.",
author = "Vassili Gelfreich and Natalia Gelfreikh",
year = "2009",
month = jul,
day = "24",
doi = "10.1088/0951-7715/22/4/006",
language = "English",
volume = "22",
pages = "783--810",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - Unique resonant normal forms for area-preserving maps at an elliptic fixed point

AU - Gelfreich, Vassili

AU - Gelfreikh, Natalia

PY - 2009/7/24

Y1 - 2009/7/24

N2 - We study possible simplifications of normal forms for area-preserving maps near a resonant elliptic fixed point. In the generic case we prove that at all orders the Takens normal form vector field can be transformed to the particularly simple form described by the formal interpolating Hamiltonian The form of formal series A and B depends on the order of the resonance n. For each n ≥ 3 we establish which terms of the series can be eliminated by a canonical substitution and derive a unique normal form which provides a full set of formal invariants with respect to canonical changes in coordinates. We extend these results to families of area-preserving maps. Then the formal interpolating Hamiltonian takes a form similar to the case of an individual map but involves formal power series in action I and the parameter.

AB - We study possible simplifications of normal forms for area-preserving maps near a resonant elliptic fixed point. In the generic case we prove that at all orders the Takens normal form vector field can be transformed to the particularly simple form described by the formal interpolating Hamiltonian The form of formal series A and B depends on the order of the resonance n. For each n ≥ 3 we establish which terms of the series can be eliminated by a canonical substitution and derive a unique normal form which provides a full set of formal invariants with respect to canonical changes in coordinates. We extend these results to families of area-preserving maps. Then the formal interpolating Hamiltonian takes a form similar to the case of an individual map but involves formal power series in action I and the parameter.

UR - http://www.scopus.com/inward/record.url?scp=67650735595&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/22/4/006

DO - 10.1088/0951-7715/22/4/006

M3 - Article

AN - SCOPUS:67650735595

VL - 22

SP - 783

EP - 810

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 4

ER -

ID: 51826948