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Introduction

Preliminaries Bifurcations in the plane

Homoclinic orbits of nonhyperbolic singular points

Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case

Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case

Bifurcations of homoclinic trajectories of hyperbolic saddles

Elements of hyperbolic theory Normal forms for local families: Hyperbolic case

Normal forms for unfoldings of saddlenodes

Bibliography

Introduction

Preliminaries Bifurcations in the plane

Homoclinic orbits of nonhyperbolic singular points

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Elements of Differential Topology

Degree in Finite-Dimensional Spaces

Leray-Schauder Degree for Compact Fields

Nussbaum-Sadovskii Degree for Condensing Fields

Applications to Bifurcation Theory

S 1 -Equivariant Degree

Global Hopf Bifurcation Theory

Equivariant Degree of Dold-Ulrich

References

Index

Elements of Differential Topology

Degree in Finite-Dimensional Spaces

Leray-Schauder Degree for Compact Fields