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1.

図書
図書
1. Smooth dynamical systems
M.C. Irwin
出版情報: Singapore : World Scientific, c2001  xii, 259 p. ; 23 cm
シリーズ名: Advanced series in nonlinear dynamics ; v. 17
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Foreword
Preface
Introduction
The simple pendulum / I.：
A dissipative system / II.：
The spherical pendulum / III.：
Vector fields and dynamical systems / IV.：
Some Simple Examples / Chapter 1.：
Flows and homeomorphisms
Orbits
Examples of dynamical systems
Constructing systems
Properties of orbits / V.：
Appendix 1
Group actions
Equivalent Systems / Chapter 2.：
Topological conjugacy
Homeomorphisms of the circle
Flow equivalence and topological equivalence
Local equivalence
Limit sets of flows
Limit sets of homeomorphisms / VI.：
Non-wandering sets / VII.：
Appendix 2
Two topological lemmas
Oriented orbits in Hausdorff spaces
Compactification
Integration of Vector Fields / Chapter 3.：
Vector fields
Velocity vector fields and integral flows
Ordinary differential equations
Local integrals
Global integrals
Appendix 3
Integrals of perturbed vector fields
First integrals
Linear Systems / Chapter 4.：
Linear flows on R[superscript n]
Linear automorphisms of R[superscript n]
The spectrum of a linear endomorphism
Hyperbolic linear automorphisms
Hyperbolic linear vector fields
Appendix 4
Spectral Theory
Linearization / Chapter 5.：
Regular points
Hartman's theorem
Hartman's theorem for flows
Hyperbolic closed orbits
Appendix 5
Smooth linearization
Liapunov stability
The index of a fixed point
Stable Manifolds / Chapter 6.：
The stable manifold at a hyperbolic fixed point of a diffeomorphism
Stable manifold theory for flows
The generalized stable manifold theorem
Appendix 6
Perturbed stable manifolds
Stable Systems / Chapter 7.：
Low dimensional systems
Anosov systems
Characterization of structural stability
Density
Omega stability
Bifurcation
Theory of Manifolds / Appendix A.：
Topological manifolds
Smooth manifolds and maps
Smooth vector bundles
The tangent bundle
Immersions, embeddings and submersions
Sections of vector bundles
Tensor bundles
Riemannian manifolds / VIII.：
Map Spaces / Appendix B.：
Spaces of smooth maps
Composition theorems
Spaces of sections
Spaces of dynamical systems
The Contraction Mapping Theorem / Appendix C.：
Bibliography
Subject Index
Foreword
Preface
Introduction
2.

図書
図書
2. From finite to infinite dimensional dynamical systems (: hard ; : pbk)
edited by J.C. Robinson and P.A. Glendinning
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xiii, 215 p. ; 25 cm
シリーズ名: NATO science series ; Sub-series II, Mathematics, physics and chemistry ; v. 19
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Preface
List of Contributors
Introduction / J.C. Robinson ; P.A. Glendinning
Spatial correlations and local fluctuations in host-parasite models / M.J. Keeling ; D.A. Rand
Lattice dynamical systems / L.A. Bunimovich ; C. Giberti
Attractors and dynamics in partial differential equations / J.K. Hale
Nonlinear dynamics of extended systems / P. Collet
Three lectures on mathematical fluid mechanics / P. Constantin
Low-dimensional models of turbulence / P.J. Holmes ; J.C. Mattingly ; R.W. Wittenberg
Preface
List of Contributors
Introduction / J.C. Robinson ; P.A. Glendinning
3.

図書
図書
3. Qualitative theory of dynamical systems : the role of stability preserving mappings. 2nd ed. , rev. and expanded
Anthony N. Michel, Kaining Wang, Bo Hu
出版情報: New York : Marcel Dekker, c2001  xv, 707 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 239
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Preface to the Second Edition
Preface to the First Edition
Introduction / 1.：
Dynamical Systems / 1.1：
Stability Preserving Mappings / 1.2：
Stability of Motion / 1.3：
Finite Dimensional Systems / 1.4：
Infinite Dimensional Systems / 1.5：
Differential Inclusions / 1.6：
Hybrid Dynamical Systems / 1.7：
Stability of Hybrid and Discontinuous Dynamical Systems / 1.8：
Case Studies in Hybrid and Discontinuous Dynamical Systems / 1.9：
Bibliography
Notation / 2.：
Ordinary Differential Equations / 2.2：
Ordinary Difference Equations / 2.4：
Ordinary Differential Inequalities / 2.5：
Ordinary Difference Inequalities / 2.6：
Functional Differential Equations / 2.7：
Volterra Integrodifferential Equations / 2.8：
Semigroups / 2.9：
Partial Differential Equations / 2.10：
Notes and References / 2.11：
Problems / 2.12：
Invariant Sets / 3.：
Qualitative Characterizations / 3.2：
Comparison Theorems / 3.3：
Applications / 3.5：
A Perspective / 3.6：
Systems of Differential and Difference Inequalities as Comparison Systems / 3.7：
Results Involving Quasimonotonicity Conditions: Continuous-Time Case / 4.2：
Results Involving Monotonicity Conditions: Discrete-Time Case / 4.3：
The Principal Lyapunov Theorems for General Dynamical Systems / 4.4：
Converse Theorems / 4.5：
Autonomous Systems / 4.6：
Invariance Theory / 4.7：
Uniqueness of Motions / 4.8：
Lyapunov Functions and Stability Preserving Mappings / 4.9：
Applications to Discrete Event Systems / 4.10：
Preliminaries / 4.11：
Stability and Boundedness / 5.2：
Instability / 5.3：
Comparison Theory / 5.4：
Applications: Absolute Stability of Regulator Systems / 5.7：
Applications to Artificial Neural Networks / 5.8：
Applications to Digital Filters / 5.9：
Hybrid Systems / 5.10：
An Application to Artificial Neural Networks with Time Delays / 6.8：
Application to a Multicore Nuclear Reactor Model / 6.9：
Stability Analysis / 6.10：
Dynamical Systems Determined by Differential Inequalities / 7.3：
Applications to Robust Stability / 7.5：
Applications to Absolute Stability of Regulator Systems / 7.6：
Applications to a Class of Nonlinear Circuits and Artificial Neural Networks / 7.7：
A Model for General Hybrid Dynamical Systems / 7.8：
Some Examples of Hybrid Dynamical Systems Defined on Generalized Time / 8.2：
Some Qualitative Characterizations of Hybrid Dynamical Systems / 8.3：
Embedding of Hybrid Dynamical Systems into Dynamical Systems Defined on Real Time R[superscript +] / 8.4：
Some Examples of Hybrid Dynamical Systems Defined on R[superscript +] / 8.5：
Stability of Discontinuous Dynamical Systems: Results Involving Stability Preserving Mappings / 8.6：
The Principal Lyapunov Theorems for Discontinuous Dynamical Systems / 9.2：
Results Involving Vector Lyapunov Functions / 9.3：
Interconnected Systems / 9.5：
Some Qualitative Properties of Sampled-Data Control Systems / 9.6：
Stability Analysis of Multirate Digital Control Systems / 10.2：
Stability Analysis of Pulse-Width-Modulated Feedback Control Systems / 10.3：
A Class of Variable Structure Systems: Hopfield Neural Nets with Infinite Gain Amplifiers / 10.4：
Dynamical Systems Subjected to State Saturation Constraints / 10.5：
Index / 10.6：
Preface to the Second Edition
Preface to the First Edition
Introduction / 1.：
4.

図書
図書
4. Global analysis of dynamical systems : Festchrift dedicated to Floris Takens for his 60th birthday
edited by Henk W Broer, Bernd Krauskopf and Gert Vegter
出版情報: Bristol, [Eng.] : Institute of Physics Pub., c2001  xiv, 464 p. ; 25 cm
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