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18 INDEX a-limit set 150 Diffeomorphism 3 Attracting set 13 Difference Equations 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 Eigenspace of flow Eigenvalues 69 - of map complex 69 - Flip real 69 - Fold 209 Eigenvectors 69 - Hopf Elementary Catastrophes Pitchford 198 Equations - saddle node Bernouilli 11 - supercritical characteristic 70 - sub critical difference 39 - transcritical differential 5 Biological control Lienard 155 Biology logistic 212 Blue Sky catastrophe Van de Pol 154 Equilibrium point 8 - Exchange of Stability 195, Feigenbaum number 214 Catastrophe Theory fold Floquet Theory cusp 233 Centre Manifold Theorem Chaos First return map in map 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 Hartman-Grobman Theorem 135 Homeomorphism 160 Degenerate 195,266 Homoclinic bifurcation 219 Determinants Homoclinic tangle 218

19 314 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 ,218 34, , 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, , , , , 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 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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