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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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Normal forms (Mathematics) --- Perturbation (Mathematics) --- Wave equation --- Numerical solutions.

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Differential geometry. Global analysis --- Chaotic behavior in systems --- Differentiable dynamical systems --- Normal forms (Mathematics) --- Congresses.

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Algèbre linéaire. --- Algebras, Linear --- Matrices --- Normal forms (Mathematics) --- Formes normales (mathématiques)

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Algebra --- Matrices --- Differential equations --- Eigenvalues --- Formes normales (mathématiques) --- Normal forms (Mathematics) --- Formes normales (mathématiques) --- Equations differentielles --- Stabilite