TABLE OF CONTENTS
PART I: UNFOLDINGS OF QUASI-PERIODIC TORI
H.W. Broer, G.B. Huitema and F. Takens
1. Introduction 1
2. Preliminaries 5
a. Invariant manifolds, normal linearization, integrability 5
b. Unfoldings of matrices 10
3. The integrable case 15
a. The general (dissipative) context 15
b. The volume preserving context 17
c. The symplectic context 17
4. The nearly integrable case in the general (dissipative) context 19
5. The nearly integrable cases in the volume preserving
and the symplectic (m = n) contexts 25
a. Addition of local parameters 25
b. The volume preserving case m = 1 26
c. The symplectic case m n 28
6. The nearly integrable case in the general symplectic context 29
a. General remarks 29
b. Normal linearization 30
c. The results 32
7. Applications-Related results 35
a. A more general stability result 35
b. Comparison with Moser's modifying terms 38
c. Fewer parameters 39
d. Applications to local bifurcation theory 46
e. A locally free Tn-action 49
f. Oscillators with quasi-periodic forcing 50
8. Proof of the main result 53
a. Introduction 53
b. Proof of Theorem 8.1 60
c. Proof of Theorem 6.1 74
Appendix
Finite differentiability 79
PART II: TOWARD A QUASI-PERIODIC BIFURCATION THEORY
B.L.J. Braaksma, H.W. Broer and G.B. Huitema
1. Introduction 83
2. A higher order normal form theory 89
a. The case m = 1 90
b. The case ra = 2 97
c. Whitney-smoothness in the frequencies 100
d. The local approach 106
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