Mathematical Physics I Flashcards
1
Q
n-th order ODE
A
.
2
Q
solution of nth order ODE
A
.
3
Q
autonomous
A
.
4
Q
initial value problem
A
.
5
Q
solution to IVP
A
.
6
Q
matrix exponential
A
.
7
Q
fixed point
A
.
8
Q
Picard-Lindeloef Theorem (versions)
A
.
9
Q
prolongation of solutions
A
.
10
Q
maximal solution
A
.
11
Q
phase space
A
.
12
Q
dynamical systems
- invertible (G is what?)
- continuous
- discrete
A
.
13
Q
flow of IVP
A
.
14
Q
lie group
A
.
15
Q
orbit
A
.
16
Q
cycle
A
.
17
Q
equilibrium point
A
.
18
Q
period
A
.
19
Q
phase portrait
A
.
20
Q
invariant set/function
A
.
21
Q
Lyapunov stable
A
.
22
Q
attracting
A
.
23
Q
asymptotically stable
A
.
24
Q
Lie theorem
A
.
25
infinitesimal transformation
.
26
Lie derivative of F along v
.
27
Theorem 2.3
.
28
Theorem 2.4
.
29
phase volume
.
30
Liouville Theorem
.
31
Poincare Theorem
.
32
Lyapunov function (strict)
.
33
Lyapunov Theorem
.
34
linear autonomous and homogeneous IVP
.
35
exponential matrix
.
36
general linear Lie algebra
.
37
Jordan normal form
.
38
generalized eigenspace
.
39
Jordanization of A
.
40
real Jordan blocks
.
41
Theorem 2.10
.
42
stable, unstable, center manifold
.
43
hyperbolic fixed point
.
44
Theorem 2.13
.
45
linearization of IVP
.
46
topologically equivalent
.
47
topologically conjugate
.
48
orbitally equivalent
.
49
Hartmann-Gromwell Theorem
.
50
standard saddle system
.
51
fundamental solution
.
52
Theorem (Abel-Liouville)
.
53
non-antonomous, non homogeneous linear IVP
.
54
periodic homogeneous IVP
.
55
monodromy matrix
.
56
Floquet multipliers
.
57
Floquet theorem
.
58
bifurcations
.
59
topological normal form
.
60
genericity conditions
.
61
topological equivalence
.
62
bifurcation point
.
63
bifurcation diagram
.
64
saddle node bifurcations
.
65
Hopf bifurcations
.
66
configuration space
.
67
mechanical system
.
68
Newton equations
.
69
potential energy
.
70
conservative system
..
71
kinetic energy
.
72
Lagrangian
.
73
differentiable functional
.
74
extremal
.
75
action functional
.
76
Lemam 3.1
.
77
Euler-Lagrange equations
.
78
Legendre condition
.
79
symmetry Lie group
.
80
momentum conjugated to p
.
81
Legendre transformation
.
82
canonical hamiltonial
.
83
divergence free
.
84
symplectic matrix
.
85
canonical symplectic vector space
.
86
symplectic Lie algebra
.
87
canonical Poisson bracket
.
88
poisson involution
.
89
canonical H. equations
.
90
canonical H. flow.
.
91
canonical Poisson structure
.
92
Poisson Theorem
.
93
canonical transformation
.
94
symplectic transformation
.
95
wedge product
.
96
differential n-form
.
97
volume form
.
98
exterior derivative
.
99
exactness property
.
100
canonical symplectic 2-form
.
101
generating functions
.
102
smooth distribution
.
103
integral manifold
.
104
integrable distribution
.
105
Froebenius Theorem
.
106
k-vector fields
.
107
Lie derivative of a 2-vector field
.
108
Cartan formula
.
109
Lie algebra
.
110
matrix Lie group
.
111
Poisson bracket
.
112
Poisson manifold
.
113
Hamiltonian VF
.
114
Casimir function
.
115
Poisson involution
.
116
rank of P. manifold
.
117
regular P. manifold
.
118
symplectic manifold
.
119
symplectic morphism
.
120
symplectic foliation dim m
.
121
Euler top
.
