Contents
Preface ... . 1
Chapter I . O n stabl e propertie s o f the solutio n se t o f a n ordinar y differentia l equa -
tion 3
1. Isolate d invariant set s and continuatio n 3
2. A n example 4
3. Th e Mors e index . 5
4. Sum s and products o f indices 7
5. A consequence o f th e su m formula 1
6. Gradient-lik e equation s 12
7. Attractors , repellers an d Mors e decomposition s 14
8. Chai n recurrent an d strongl y gradient-lik e flow s 16
9. Som e example s o f "bifurcation " 18
10. Concludin g remarks 2 2
Chapter II . Elementar y propertie s o f flows 2 4
1. Flow s an d differentia l equation s 2 4
2. Flow s an d th e theore m o f Wazewski 2 4
3. Th e translatio n flo w o n the spac e of curve s 2 7
4. Limi t sets , nonwandering set s and compact invarian t set s 2 9
5. Attractor-repelle r pair s 3 2
6. Chai n recurrenc e 3 6
7. Mors e decomposition s 4 0
Chapter III . Th e Morse index 4 3
1. Introductio n 4 3
2. Definition s fro m homotop y theor y 4 3
3. Loca l flow s an d isolate d invarian t set s 4 4
4. Inde x pair s 4 6
5. Th e Morse index 5 0
6. Computin g th e homotop y inde x 5 3
7. Connection s 6 0
8. Concludin g remark s 6 3
Chapter IV . Continuatio n 6 4
1. Th e space o f isolate d invarian t set s 6 4
2. Continuatio n o f I(S) 6 8
3. Continuatio n o f connection s an d Mors e decomposition s . , 7 2
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