280 Index chain transitive set, 51, 60 and time reversal, 53, 61 for time shift, 200 maximal, 51, 58, 60 characteristic number, 99 cocycle, 114, 120 2-parameter, 102, 118, 131 linear periodic difference equation, 131 linear topological system, 170 random linear, 225, 231 conjugacy and chain transitivity, 54, 63 and fixed points, 32 and limit sets, 54 and Morse decompositions, 156 and periodic solutions, 32 and structural stability, 34 dynamical systems, 32, 39 in projective space, 79 linear, 33 linear autonomous differential equations, 33 linear contractions, 41 linear difference equations, 43 projective flows, 75, 77 smooth, 32, 33, 39 Conley index, 66 connected component, 57 control system, 117 bilinear, 171, 197 linear, 171 cycles, 156 cylinder sets, 226 dynamical system continuous, 30, 38 linear skew product, 120, 121, 231 bilinear control system, 201 periodic difference equation, 131 robust linear system, 201 metric, 117, 121, 224 random linear, 117, 121, 230 topological linear, 170 eigenspace, 6 complex generalized, 6 random, 258 real, 9 real generalized, 9, 26 eigenvalue stability, 16, 24, 109, 128, 137 equilibrium, 31 equivalence of flows, 45 ergodic flow, 227 ergodic map, 212 uniquely, 221 evaluation map, 116 exponential growth rate finite time, 172 linear autonomous difference equation, 20 linear autonomous differential equation, 12 linear periodic difference equation, 128, 131, 132 linear periodic differential equation, 137, 139 linear topological flow, 172, 173, 192 of a function, 121, 123 volume, 87, 88, 90 exterior power, 238 exterior product, 85 Fatouâ€™s lemma, 219 Fenichelâ€™s uniformity lemma, 175 fiber, 170 Fibonacci numbers, 78 fixed point, 31 asymptotically stable, 16, 23 exponentially stable, 16, 24 stable, 16, 23 unstable, 16, 24 flag manifold, 95, 240 metric, 240 flag of subspaces, 240, 247 linear autonomous difference equation, 22 linear autonomous differential equation, 15, 71 linear periodic difference equation, 133 linear periodic differential equation, 141 random, 258 Floquet exponent, 128, 137 Floquet multiplier, 128, 137 Floquet space, 132, 139 Floquet theory, 127, 174, 228 flow continuous, 30 ergodic, 227 linear skew product, 114 structurally stable, 34

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