.

0 (hodnocen0 x )

BK

Bristol : A. Hilger, 1991

viii, 293 s.

ISBN 0-7503-0150-3

000032206

INTRODUCTION vii // I SELECTED READING ON THE FOUNDATIONS OF ALGEBRA, // TOPOLOGY, MATHEMATICAL ANALYSIS AND THE THEORY // OF DIFFERENTIAL EQUATIONS 1 // 1.1 Some basic concepts and notation 1 // 1.2 Relations on a set 2 // 1.3 Linear, Euclidean and linear normed spaces 3 // 1.4 Metric spaces 5 // 1.5 Topological spaces 5 // 1.6 Matrices 9 // 1.7 Linear mappings 10 // 1.8 Mathematical analysis 12 // 1.9 Differential equations 18 // 2 FOUNDATIONS OF THE THEORY OF DIFFERENTIABLE MANIFOLDS AND DIFFERENTIABLE MAPPINGS 22 // 2.1 Cr -manifolds 22 // 2.2 CT-mappings 26 // 2.3 Tangent space to a CT-manifold 27 // 2.4 CF-submanifolds 32 // 2.5 CT-manifolds in Rn 35 // 2.6 Immersion and submersion theorems 36 // 2.7 Regular and critical values of mappings 39 // 2.8 Topology on the space of CT-mappings 41 // 2.9 Jets 45 // 2.10 Transversality 46 // 2.11 Stratification of algebraic and semi-algebraic manifolds. 55 // 2.12 Transversality to stratification 61 // 3 VECTOR FIELDS AND DYNAMICAL SYSTEMS 63 // 3.1 Vector fields on differentiable manifolds 63 // 3.2 Limit properties of dynamical systems 75 // 3.3 Examples of vector fields 84 // 3.4 Generic properties of parameter-dependent matrices 86 // 3.5 Linear dynamical systems and some notions from the theory // of non-linear dynamical systems 103 // 3.6 Grobman-Hartman Theorem 128 // 3.7 Normal forms of differential equations 143 // 3.8 Poincare mapping 159 // 4 INVARIANT MANIFOLDS 172 // 4.1 Stable and unstable manifolds 172 // 4.2 Centre manifolds 183 // 5 GENERIC BIFURCATIONS OF VECTOR FIELDS AND // DIFFEOMORPHISMS 203 // 5.1 Ljapunov-Schmidt Method 203 // 5.2 Generic bifurcations of 1-parameter systems of vector fields in neighbourhoods of singular points 214 // 5.3 Generic bifurcations of 1-parameter systems of diffeomorphisms 238 //

5.4 Generic bifurcations of 1-parameter systems of vector fields in neighbourhoods of periodic trajectories 258 // 6 COMPLEMENTARY NOTES ON THE CONTEMPORARY // THEORY OF DYNAMICAL SYSTEMS 262 // 6.1 Generic bifurcations of multi-parameter systems of // vector fields 262 // 6.2 Global theory of dynamical systems 270 // 6.3 Šilnikov bifurcation 273 // 6.4 Global Hopf bifurcation 276 // 6.5 Attractors and chaotic sets 279 // REFERENCES 282 // SUBJECT INDEX 289