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Ordinary differential equations --- Differential geometry. Global analysis --- Functional differential equations --- Bifurcation theory --- Manifolds (Mathematics) --- Equations différentielles fonctionnelles --- Théorie de la bifurcation --- Variétés (Mathématiques) --- 517.987 --- Geometry, Differential --- Topology --- Differential equations, Functional --- Differential equations --- Functional equations --- Differential equations, Nonlinear --- Stability --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Numerical solutions --- Bifurcation theory. --- Functional differential equations. --- Manifolds (Mathematics). --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Equations différentielles fonctionnelles --- Théorie de la bifurcation --- Variétés (Mathématiques)

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Differential geometry. Global analysis

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This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3-5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations with one, two or several parameters. This book is aimed at mathematicians and graduate students interested in dynamical systems, ordinary differential equations and/or bifurcation theory. The basic knowledge required by this book is advanced calculus, functional analysis and qualitative theory of ordinary differential equations.

Bifurcation theory. --- Vector fields. --- Normal forms (Mathematics)

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Differential equations