x NOTATION
a projection
gc
» t
c
along t
x c
(p. 12);
a1-
projection
gc
t^
c
along t
c
(p. 12)
a* projection g* —• » t along
t"1
(p. 56)
£ element of so(3, C) defined through
£u = £x u, for
^ G C 3
(p. 13)
{u, v} Poisson bracket of u and i; (p. 13)
£M infinitesimal generator of action of G on M,
along some ( e g
P symplectic manifold
J momentum map of G-action on P
J^ (-component of J (p. 15)
JG
momentum map of G-action on G x to (p. 16);
in Part 2, momentum map of G-action on G x tj (p. 55)
j
G
momentum map of T-action on G x to (p. 22);
in Part 2, momentum map of T-action on G x tj (p. 55)
ft frequency (=V/z) (p. 21)
IT integral lattice of torus T in t (p. 22)
H T-average of H (p. 23)
int M interior of M
Av(M)
space of continuous maps u : M V that are real-analytic
(resp. holomorphic) on int M, for a real (resp. complex)
vector space V (p. 26)
|| || supremum norm on
Av
(M) (p. 26)
closed i?-ball in t with center p (p. 27)
closed p-neighborhood of BR(P) in
tc(p.
27)
Hamiltonian analyticity widths (p. 27)
fixed element of t0 (or U C t0 (pp. 27,42)
variable parameters (p* G int 5 ) (p. 28)
shorthand for Bp(p) and Bp(jp) (see above)
the domain G^ x
B?r/(p*)
(p. 28)
BR(P)
BpRip)
a, /?
P
B, BP
7
Dy{P*,P)
C i , . . .
E
\-\s
fel,fe2,
a i , . . .
ft
Q l ,
. . .
n^-
c
7To
7TW
,c7
^ 3
ak
)
supremum norm on Ac""(p*,r)) (D1V (p. 28)
r/9
time constants (p. 29)
dimensionless constants (pp. 28-30)
energy constant (= ap/T^j) (p. 30)
norm on C
n c X n G
induced by Schur-Hadamard
product S (p. 32)
dimensionless constants (pp. 32,36)
number of positive roots of g in t* (p. 32)
positive real roots of g in t* (p. 32)
isomorphism t t* induced by Killing form (p. 33)
inner product on t* induced by Killing form (p. 33)
inverse roots g in t (p. 33)
Cartan integers of g (p. 33)
see p. 33
dimensionless constant (p. 39)
set of points in M not in Z
projection g*eg O {O a co-adjoint orbit; p. 47)
projection g*eg - W (p. 47)
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