Research output: Contribution to journal › Article › peer-review
Unique resonant normal forms for area-preserving maps at an elliptic fixed point. / Gelfreich, Vassili; Gelfreikh, Natalia.
In: Nonlinearity, Vol. 22, No. 4, 24.07.2009, p. 783-810.Research output: Contribution to journal › Article › peer-review
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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