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

共 50 条

[41] Positive partial realization problem for linear discrete-time systems
Kaczorek, Tadeusz
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2007, 17 (02) : 165 - 171
[42] Reachability realization and stabilizability of switched linear discrete-time systems
Xie, GM
Wang, L
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 280 (02) : 209 - 220
[43] Positive Realization of Stable Fractional Discrete-Time Linear Systems
Sajewski, Lukasz
ASIAN JOURNAL OF CONTROL, 2014, 16 (03) : 922 - 927
[44] On stability of discrete-time systems under nonlinear time-varying perturbations
Pham Huu Anh Ngoc
Le Trung Hieu
Advances in Difference Equations, 2012
[45] On stability of discrete-time systems under nonlinear time-varying perturbations
Pham Huu Anh Ngoc
Le Trung Hieu
ADVANCES IN DIFFERENCE EQUATIONS, 2012,
[46] SOLUTIONS OF CONTINUOUS-TIME SYSTEMS BY THE DISCRETE METHODS
Svarc, Ivan
APLIMAT 2005 - 4TH INTERNATIONAL CONFERENCE, PT II, 2005, : 153 - 159
[47] INHERITANCE OF MINIMALITY FROM CONTINUOUS TO DISCRETE TIME SYSTEMS
Hric, Roman
Snoha, Eubomir
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2024, 44 (12) : 3962 - 3979
[48] Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time
Lassi Paunonen
David Seifert
Journal of Dynamics and Differential Equations, 2018, 30 : 433 - 445
[49] DISCRETE APPROXIMATION OF CONTINUOUS-TIME SYSTEMS - A SURVEY
KOWALCZUK, Z
IEE PROCEEDINGS-G CIRCUITS DEVICES AND SYSTEMS, 1993, 140 (04): : 264 - 278
[50] The discrete methods for solutions of continuous-time systems
Svarc, I.
RECENT ADVANCES IN MECHATRONICS, 2007, : 180 - +

← 1 2 3 4 5 →