Index 283 existence, 30 linear autonomous difference equation, 18 linear autonomous differential equation, 4 periodic, 31 solution formula in Jordan block, 11, 12, 19, 20 in projective space, 71, 73, 77 on the sphere, 78, 203 scalar differential equation, 101 solution map continuity, 5, 18, 104, 119 continuity with respect to parameters, 104, 119 spectrum eigenvalues of a matrix, 6 Lyapunov spectrum, 204 Lyapunov spectrum for a random system, 228 Morse spectrum, 172, 204 uniform growth spectrum, 195 stability and eigenvalues, 16, 24, 109, 152 asymptotic, 16, 24, 135, 143, 177 exponential, 16, 24, 135, 143, 177, 205 almost sure, 229, 232 stability diagram linear oscillator with uncertain restoring force, 205, 207 Mathieu equation, 150 random linear oscillator, 265 stability radius, 206 stable fixed point, 16, 23 stable subbundle, 175, 177 linear periodic difference equation, 135 linear periodic differential equation, 143 random linear system, 229, 232 robust linear system, 205 stable subspace linear autonomous difference equation, 24 linear autonomous differential equation, 16 linear periodic difference equation, 135 linear periodic differential equation, 143 random linear system, 229, 232 stochastic differential equation, 265 stochastic linear differential equation, 226, 269 subadditive ergodic theorem, 217 subadditive sequence, 244 subbundle, 171 exponentially separated, 189, 190 Theon of Smyrna, 78 theorem Arzel´ a-Ascoli, 115 Banach’s fixed point, 102 Birkhoff’s Ergodic, 214 Blaschke’s, 55 Furstenberg-Kesten, 252 invariance of domain, 38 Jordan curve, 209 Kingman’s subadditive ergodic, 217 Lebesgue’s on dominated convergence, 104 maximal ergodic, 213 Multiplicative Ergodic, 227, 231 deterministic, 242 Oseledets’, 227, 231 Poincar´ e-Bendixson, 65 Selgrade’s, 182 time shift, 115, 200 time-n map, 38 time-t map, 30 time-one map, 120 time-reversed equation, 13 linear difference equation, 21 time-reversed flow, 60, 187, 194 and chain transitivity, 53, 61 and limit sets, 50 time-varying perturbation, 117 topology uniform convergence, 115 type number, 123 uniform growth spectrum, 195 uniquely ergodic map, 221 unstable subbundle, 175 linear periodic difference equation, 135 linear periodic differential equation, 143 random linear system, 229, 232 robust linear system, 205 unstable subspace linear autonomous difference equation, 24
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