Measure expansivity for C1-conservative systems

被引：4

作者：

Ahn, Jiweon ^{[1
]}

Lee, Manseob ^{[2
]}

Oh, Jumi ^{[1
]}

机构：

[1] Chungnam Natl Univ, Dept Math, Daejeon 305764, South Korea

[2] Mokwon Univ, Dept Math, Daejeon 302729, South Korea

来源：

CHAOS SOLITONS & FRACTALS | 2015年 / 81卷

基金：

新加坡国家研究基金会;

关键词：

Expansive; Measure expansive; Volume preserving diffeomorphisms; Divergence free vector fields; Anosov; STABILITY; DIFFEOMORPHISMS;

D O I：

10.1016/j.chaos.2015.10.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the notion of measure expansivity for volume preserving diffeomorphisms and divergence free vector fields. We prove that the following three theorems. (1) The C-1-interior of measure expansive volume preserving diffeomorphism is Anosov. (2) A C-1-generic volume preserving diffeomorphism is Anosov. (3) The C-1-interior of measure expansive divergence free vector field is Anosov. (C) 2015 Elsevier Ltd. All rights reseived,

引用

页码：400 / 405

页数：6

共 50 条

[31] ACCURATE NUMERICAL DISCRETIZATIONS OF NON-CONSERVATIVE HYPERBOLIC SYSTEMS [J].

Fjordholm, Ulrik Skre ;

Mishra, Siddhartha .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (01) :187-206

[32] Less conservative conditions for asymptotic stability of impulsive control systems [J].

Sun, JT ;

Zhang, YP ;

Wu, QD .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (05) :829-831

[33] Stability and response bounds of non-conservative linear systems [J].

W. Kliem ;

C. Pommer .

Archive of Applied Mechanics, 2004, 73 :627-637

[34] Controllability and Observability of Uncertain Systems: A Robust Measure [J].

Sojoudi, Somayeh ;

Lavaei, Javad ;

Aghdam, Amir G. .

PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, :4180-4186

[35] A sufficient condition for instability of equilibrium of non-conservative undamped systems [J].

Bulatovic, R. M. .

PHYSICS LETTERS A, 2011, 375 (44) :3826-3828

[36] Decomposition and Uncoupling of Multi-Degree-of-Freedom Gyroscopic Conservative Systems [J].

Bulatovic, Ranislav M. ;

Udwadia, Firdaus E. .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2024, 91 (03)

[37] Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems [J].

Biswas, Abhijit ;

Ketcheson, David I. I. .

JOURNAL OF SCIENTIFIC COMPUTING, 2023, 97 (01)

[38] A class of linearly implicit energy-preserving schemes for conservative systems [J].

Li, Xicui ;

Wang, Bin ;

Zou, Xin .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 537 (01)

[39] A less conservative robust control method for a class of nonpassive uncertain systems [J].

Akiba, Junpei ;

Liu, Kang-Zhi ;

Qiu, Li ;

Yu, Pan ;

Koiwa, Kenta ;

Zanma, Tadanao .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2022, 32 (02) :682-697

[40] Stabilization of linear conservative dynamical systems using cyclic energy dissipation [J].

Michel, Anthony N. ;

Hou, Ling .

49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, :1553-1558

← 1 2 3 4 5 →