**Memoirs of the American Mathematical Society**

1996;
128 pp;
Softcover

MSC: Primary 34;
Secondary 58

Print ISBN: 978-0-8218-0441-4

Product Code: MEMO/121/578

List Price: $46.00

Individual Member Price: $27.60

**Electronic ISBN: 978-1-4704-0163-4
Product Code: MEMO/121/578.E**

List Price: $46.00

Individual Member Price: $27.60

# Global Aspects of Homoclinic Bifurcations of Vector Fields

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*Ale Jan Homburg*

In this book, the author investigates a class of smooth
one parameter families of vector fields on some
\(n\)-dimensional manifold, exhibiting a homoclinic bifurcation.
That is, he considers generic families \(x_\mu\), where
\(x_0\) has a distinguished hyperbolic singularity \(p\)
and a homoclinic orbit; an orbit converging to \(p\) both for
positive and negative time. It is assumed that this homoclinic orbit is
of saddle-saddle type, characterized by the existence of
well-defined directions along which it converges to the
singularity \(p\).

The study is not confined to a small neighborhood of the
homoclinic orbit. Instead, the position of the stable and unstable set
of the homoclinic orbit is incorporated and it is shown that
homoclinic bifurcations can lead to complicated bifurcations and
dynamics, including phenomena like intermittency and annihilation of
suspended horseshoes.

#### Readership

Graduate students and research mathematicians interested in differential equations.