REALIZATION OF TANGENT PERTURBATIONS IN DISCRETE AND CONTINUOUS TIME CONSERVATIVE SYSTEMS

被引：8

作者：

Alishah, Hassan Najafi ^{[1
]}

Dias, Joao Lopes ^{[2
,3
]}

机构：

[1] Univ Lisbon, Fac Ciencias, CMAF, P-1749016 Lisbon, Portugal

[2] Univ Lisbon, Dept Matemat, P-1200781 Lisbon, Portugal

[3] Univ Lisbon, CEMAPRE, ISEG, P-1200781 Lisbon, Portugal

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 12期

关键词：

Franks lemma; symplectic and Hamiltonian C-1 perturbations; Poisson Hamiltonian flowbox coordinates; POSITIVE TOPOLOGICAL-ENTROPY; PARTIAL HYPERBOLICITY; GEODESIC-FLOWS; EQUATIONS; INTEGRABILITY; DYNAMICS;

D O I：

10.3934/dcds.2014.34.5359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a C-1-close Poisson diffeomorphism. We also show that a similar property holds for the Poincare map of a Hamiltonian on a Poisson manifold. These results are the conservative counterparts of the Franks lemma, a perturbation tool used in several contexts most notably in the theory of smooth dynamical systems.

引用

页码：5359 / 5374

页数：16

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