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| List of Figures | |
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| Preface | |
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| Acknowledgments | |
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| Foreword | |
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| Geometric Methods | |
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| On global bifurcation theory | |
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| Local bifurcations of limit cycles | |
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| On methods of the study of limit cycles | |
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| Geometric methods of bifurcations theory | |
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| Erugin's two-isocline method | |
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| On the method of isoclines | |
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| Isocline portraits | |
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| Classification of singular points | |
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| Other applications of the two-isocline method | |
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| The problem of center and focus | |
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| On the distinguishing problem | |
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| Lyapunov's focus quantities | |
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| Classification of symmetric cases | |
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| Geometric interpretation of quadratic centers | |
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| Poincare's topographical systems | |
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| Basic definitions | |
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| Construction of topographical systems | |
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| Topographical systems and limit cycles | |
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| On the control of semi-stable limit cycles | |
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| Canonical systems with limit cycles | |
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| Systems with field-rotation parameters | |
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| Reduction of quadratic systems | |
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| Andronov-Hopf Bifurcation | |
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| On the Andronov-Hopf bifurcation | |
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| On the history of the bifurcation | |
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| Bautin's result | |
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| The example by Shi Sonling | |
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| The example by E. A. Andronova | |
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| Construction of systems | |
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| Canonical systems with two singular points | |
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| Properties of the canonical systems | |
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| Bifurcations of limit cycles | |
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| Bifurcations of algebraic limit cycles | |
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| The case of a saddle and an antisaddle | |
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| A quadratic system with four limit cycles | |
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| Asymptotic behavior of limit cycles | |
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| Numerical results | |
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| Classification of Separatrix Cycles | |
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| On separatrix cycles | |
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| Dulac's theorem | |
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| Existential problem | |
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| On application of canonical systems | |
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| One saddle and three antisaddles (the first case) | |
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| One saddle and three antisaddles (the second case) | |
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| Classification of separatrix cycles | |
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| Other cases of singular points | |
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| The complete classification | |
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| Multiple Limit Cycles | |
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| On multiple limit cycles | |
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| Local analysis of one-parameter families | |
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| Basic notions | |
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| Multiple limit cycles and Puiseux series | |
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| Arches and paths of limit cycles | |
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| Global analysis of one-parameter families | |
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| Planar termination principle | |
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| The proof of the principle | |
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| Bifurcation surfaces of multiple limit cycles | |
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| Fold and cusp bifurcation surfaces | |
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| A swallow-tail bifurcation surface | |
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| General bifurcation surfaces | |
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| Wintner-Perko termination principle | |
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| General discussion | |
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| Monotonic families and rotated vector fields | |
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| The limit cycle problem for quadratic systems | |
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| Applications, Open Problems, Alternatives | |
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| On polynomial models of dynamical systems | |
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| A generalized Lotka-Volterra system | |
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| Some open problems of qualitative theory | |
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| Abelian integrals and limit cycles | |
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| On a work by N. P. Erugin | |
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| References | |
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| Index | |