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INDEX a-limit set 150 Diffeomorphism 3 Attracting set 13 Difference Equations 39-58 Attractors 13 Differential Equations 5-38 Asymptotic stability 100 Differential Operator D 19 Diagonalization 76 Bendixson-Poincare 151 Discrete Systems 115 Bernouilli equation 11 Bifurcation 195-210 Eigenspace 145 - of flow 195-200 Eigenvalues 69 - of map 209-210 - complex 69 - Flip 210 - real 69 - Fold 209 Eigenvectors 69 - Hopf 200-204 Elementary Catastrophes 232 - Pitchford 198 Equations - saddle node 197 - Bernouilli 11 - supercritical 198 - characteristic 70 - sub critical 197 - difference 39 - transcritical 197 - differential 5 Biological control 293 - Lienard 155 Biology 280 - logistic 212 Blue Sky catastrophe 220 - Van de Pol 154 Equilibrium point 8 - Exchange of Stability 195, 196 - Feigenbaum number 214 Catastrophe Theory 226 - fold 232 - Floquet Theory 185 - cusp 233 Centre Manifold Theorem 187-191 Chaos 211-226 First return map 183 - in map 212-216 Flow 2 - in flow 216 Focus 102 Characteristic exponent 185, 186 Fundamental Matrix- 98 Characteristic equation 70 Characteristic polynomial 70 Gradient systems 163 Codimension 229 Growth models Competing species 288 in Economics 178,258 Complex eigenvalues 93, 120 Conservative Hamiltonian Systems 171 Cusp 233 Cycle 149 Hamiltonian flow 171 Hamiltonian function 170 Hamiltonian system 170-175 Hartman-Grobman Theorem 135 Homeomorphism 160 Degenerate 195,266 Homoclinic bifurcation 219 Determinants 65-67 Homoclinic tangle 218
314 Hopf bifurcation Horseshoe map Hyperbolic fixed point Implicit Function Theorem Improper Node Idempotent matrices Intermittency IS-LM economic models Jordan canonical form Lagrangian Dynamic System Laplace transformation Li-York Theorem Liapunov - characteristic exponent - function - Second method - stability Liapunov-Smith reduction Lienard-Smith reduction Lienard system Limit Cycles Linearization theorem Manifold Map Melkinov theory Maximum Principle Morse set 200 218 136 195 104 81 217,218 34, 107 79 167 29 215 221 101 101 101 193 193 155 149 134-146 187, 188 157 219 245 245 Multiplier-accelerator models 54 Potential functions Prey-predator models Repeller Saddle loop connection Saddle node Schwarzian derivative Sensitive dependence on initial conditions Silnikov Theory Singularity Smale-Birkhoff Smale horseshoe Splitting Lemma Stabilization Control models Stability - asymptotic - local asymptotic - global asymptotic - structural 163, 226 140, 285 13 218 197 212 217,218 221, 225 195, 241 218 218 228 253 159 100 100 160 Tatonnement Model 277 Transversality Conditions 248 Unfolding 229, 241 Unimodal Map 212 Universal Constant: Feigenbaum 214 Nilpotent matrix 87, 91 Normal forms 191 Nonhyperbolic fixed points 187,195 Nonlinear Systems 133-161 Optimal Control 245 Optimal Economic growth 258 Peixoto Theorem 160 Poincare-Bendixson Theorem 151 Poincare map 183, 184 Poincare section 183
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