**CBMS Regional Conference Series in Mathematics**

Volume: 38;
1978;
89 pp;
Softcover

MSC: Primary 58;
Secondary 34; 35

Print ISBN: 978-0-8218-1688-2

Product Code: CBMS/38

List Price: $29.00

Individual Price: $23.20

**Electronic ISBN: 978-1-4704-2398-8
Product Code: CBMS/38.E**

List Price: $29.00

Individual Price: $23.20

# Isolated Invariant Sets and the Morse Index

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*Charles Conley*

A co-publication of the AMS and CBMS

This volume contains lectures from the Conference Board of
Mathematical Sciences meeting held at the University of Colorado on May
31–June 4, 1976.

The lectures consist of an expository discussion of basic results for
topological flows and a somewhat more detailed discussion of isolated invariant
sets and continuation.

The construction of the index for isolated invariant sets is new and allows
more general application than previous ones. Also, the index itself is endowed
with more structure and the continuation theorem is modified to take this new
structure into account.

Some elementary applications are given, but the main emphasis is on the
abstract theory.

#### Readership

#### Reviews & Endorsements

Every once in a while in mathematics, a strikingly original work appears which radically changes a particular field … [this book] fits this description, the area being the qualitative theory of nonlinear differential equations.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Isolated Invariant Sets and the Morse Index

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface 110 free
- Chapter I. On stable properties of the solution set of an ordinary differential equation 312 free
- 1. Isolated invariant sets and continuation 312
- 2. An example 413
- 3. The Morse index 514
- 4. Sums and products of indices 716
- 5. A consequence of the sum formula 1120
- 6. Gradient-like equations 1221
- 7. Attractors, repellers and Morse decompositions 1423
- 8. Chain recurrent and strongly gradient-like flows 1625
- 9. Some examples of "bifurcation" 1827
- 10. Concluding remarks 2231

- Chapter II. Elementary properties of flows 2433
- Chapter III. The Morse index 4352
- Chapter IV. Continuation 6473
- 1. The space of isolated invariant sets 6473
- 2. Continuation of I(S) 6877
- 3. Continuation of connections and Morse decompositions 7281
- 4. Cohomological aspects of structure 7483
- 5. Churchill's sequence, Montgomery's formulation and the Morse-Smale theorem 7685
- 6. Remarks about local flows defined by equations other than integral equations 7988
- 7. Flows with special properties 8291
- 8. Concluding remarks 8392

- Bibliography 8594
- Back Cover Back Cover1101