Index
a-contraction, 14, 37
examples of an, 15, 16, 37
a-limit set, 8, 35
age-dependent populations, 155fF.
attractor of, 159
semigroup of, 158, 159
asymptotically smooth, 4, 11, 36
collectively, 21, 41
process, 42
attract, 9
attractor,
approximation of the, 170
capacity of the, 27, 28
definition of an, 1, 17, 39
existence of an, 5, 19, 39, 40, 46
global, 1, 17, 39
Hausdorff dimension of an, 27, 28
local, 17, 160
lower-semicontinuity of the, 171
smoothness of flow on the, 56, 57
upper-semicontinuity of the, 22, 41, 52,
163, 165, 167
beam equation, 148
attractor of a, 149
periodically forced, 151
/^-condensing, 14
/^-contraction,
definition of, 14, 36
examples of a, 15
capacity, 27
finiteness of, 27
completely continuous, 13, 36
process, 42
continuity of the attractor, 53, 173
dimension, Hausdorff, 26
finiteness of, 27, 28
dissipative,
bounded, 1, 16, 38
compact, 16, 38
in two spaces, 28rT., 54ff., 120ff., 148
locally compact, 16, 38
point, 1, 16, 38
distance from B to A, 17
S(B, A), 17
equilibrium point,
definition of, 39
existence of, 40
hyperbolic, 49
stability of, 47, 48
equivalent, 25
evolutionary equations,
abstract, 120ff.
sectorial, 71ff.
semigroups of, 73, 120, 121, 122
strongly damped, 146
fixed point,
existence of a, 23, 25
hyperbolic, 25
global attractor,
definition of, 1, 17
existence of a, 5, 19, 39, 40, 42
gradient system,
definition of a, 49
attractor of a, 51, 52
Hausdorff dimension, 26
finiteness of, 27, 28
hyperbolic, 25
inertial manifold, 169, 176
invariant set,
definition of, 9, 36
isolated, 11, 38
maximal compact, 17, 38
Kuramoto-Sivashinsky equation, 153
attractor of the, 154
lower-semicontinuity, 171fT.
maps,
asymptotically smooth, 4, 11, 36
a-contracting, 14
/3-condensing, 14, 37
/^-contracting, 14, 37
maximal compact invariant set,
definition of, 17, 38
existence of, 17, 39
measure of noncompactness, 13
Kuratowskii, 13
Morse decomposition, 68
197
Previous Page Next Page