TAILIEUCHUNG - Báo cáo "On stability of Lyapunov exponents "

In this paper we consider the upper (lower) - stability of Lyapunov exponents of linear differential equations in Rn . Sufficient conditions for the upper - stability of maximal exponent of linear systems under linear perturbations are given. The obtained results are extended to the system with nonlinear perturbations. | VNU Journal of Science Mathematics - Physics 24 2008 73-80 On stability of Lyapunov exponents Nguyen Sinh Bay1 Tran Thi Anh Hoa2 1 Department of Mathematics Vietnam University of Commerces Ho Tung Mau Hanoi Vietnam 2456 Minh Khai Hanoi Vietnam Received 21 March 2008 received in revised form 9 April 2008 Abstract. In this paper we consider the upper lower - stability of Lyapunov exponents of linear differential equations in Rn. Sufficient conditions for the upper - stability of maximal exponent of linear systems under linear perturbations are given. The obtained results are extended to the system with nonlinear perturbations. Keywork Lyapunov exponents upper lower - stability maximal exponent. 1. Introduction Let us consider a linear system of differential equations x A t x t t0 0. 1 where A t is a real n X n - matrix function continuous and bounded on to to . It is well known that the above assumption guarantees the boundesness of the Lyapunov exponents of system 1 . Denote by X1 X2 . Xn X1 X2 . Xn the Lyapunov exponents of system 1 . Definition 1. The maximal exponent Xn of system 1 is said to be upper - stable if for any given e 0 there exists ỗ ỗ e 0 such that for any continuous on t0 n X n - matrix B t satisfying B t II ỗ the maximal exponent hn of perturbed system x A t B f x 2 satisfies the inequality Vn. Xn Ễ. 3 If B t II ỗ implies h1 X1 e we say that the minimal exponent X1 of system 1 is lower -stable. In general the maximal minimal exponent of system 1 is not always upper lower - stable 1 . However if system 1 is redusible in the Lyapunov sense then its maximal minimal exponent is upper lower - stable. In particular if system 1 is periodic then it has this property 2 3 . A problem arises In what conditions the maximal minimal exponent of nonreducible systems is upper lower - stable The aim of this paper is to show a class of nonreducible systems having this property. Corresponding author. E-mail nsbay@ 73 74 . Bay . Hoa VNU Journal of .

• Báo cáo khoa học
• Lyapunov exponents
• Mathematics
• Physics
• Scientific reports
• scientific studies
• natural sciences
• subjects of mathematics
• science reports
• studied mathematics
• scientific research
• Vietnam Journal of Mechanics
• On a form of lyapunov exponents
• Establishment of the form
• The disturbance direction
• The disturbance norm
• Asymptotic stability
• Positive homogeneous
• Homogeneous lattices
• Local Lyapunov exponents
• Chaotic systems
• Fractional order systems
• Human behavior
• Love dynamics
• Field programmable gate arrays
• Giới thiệu Thư viện số
• Natural Sciences Digital Library
• Thư viện số
• Digital Library
• Bộ sưu tập Thư viện số
• Summary of Doctoral Thesis
• Educational Sciences
• Methodology in Biology
• Developing textbooks’ models
• Orientation of competency development
• Methods of teaching natural science
• Annals of Agricultural Sciences
• Agricultural Sciences
• Khoa học nông nghiệp
• Natural preservatives
• Cold storage
• the natural sciences
• the social sciences
• conduct and misconduct
• Misconduct and why it occurs
• misconduct affecting
• the truth claims
• Molecular cryocrystal
• Elastic moduli
• Elastic wave
• Elastic constants
• Mathematical sciences
• Physical sciences
• Sciences
• GMAT
• math test
• McGraw Hills GMAT
• Environmental sciences
• Earth sciences
• Natural organic matters removal
• Water purification
• DBPs control
• Technology sciences
• Vecny este epoxy alkyd
• Tính chất điện
• Độ bền dung môi
• Độ bền nhiệt
• Detailed checklist
• Field labels
• Grammitid specimens
• VNU University of Science
• Xác định biên
• Dị thường từ
• Dị thường trọng lực
• Bắc Việt Nam
• Mỡ cá tra
• Etyl cacboxylate
• Etyl biodiesel
• Este axit omega 3 6 9
• Phương pháp đồng dung môi
• Đồng dung môi
• Hợp chất chứa dị vòng
• Chất xúc tác
• Phản ứng Sonogashira
• Hợp chất dị vòng năm cạnh
• Phản ứng Click
• Nano đồng
• Nano silica
• Khả năng kháng nấm
• Pyricularia oryzae
• Rhizoctonia solani
• Phân loại thực vật
• Lạng Sơn
• Aspidistra papillata
• Plant taxonomy
• Arachniodes simplicior
• Flora of Vietnam
• New record
• Phản ứng ngưng tụ croton
• Hoạt tính kháng khuẩn
• Chương trình PASS
• Dẫn xuất thiopodand
• Vật liệu nano
• Tính chất quang
• Tính chất từ
• Vật liệu nano HoFeO3
• Cảm biến miễn dịch điện hóa
• Kháng thể IgY
• Virus Newcastle
• Bình phản ứng mini
• Xúc tác lưỡng kim loại Co2Cu2
• CI NEB cơ chế phản ứng
• Phản ứng hydrogen hóa carbon monoxide
• Bọ rùa hai mảng đỏ
• Lemnia biplagiata
• Tỷ lệ sống sót
• Tỷ lệ vào nhộng
• Năng ăn con mồi
• Chất lượng nước
• Động vật nổi
• Thành phần loài
• Kênh Bún Xáng
• Đa dạng sinh học
• Camphor
• science and technology
• research projects
• Natural resources
• Research
• Natural radioactivity
• Major and accessory minerals
• Gamma ray spectrometry
• Wall rock granitoids
• Natural sciences and Technology
• Immune cells expansion
• Peripheral blood
• Immune cell therapy
• Natural killer cells
• Cytotoxic T lymphocytes
• Peripheral blood mononuclear cells