Catastrophe Theory for Scientists and EngineersThis advanced-level treatment describes the mathematics of catastrophe theory and its applications to problems in mathematics, physics, chemistry and engineering. 28 tables. 397 black-and-white illustrations. 1981 edition. |
Contents
PART | 3 |
The Local Character of Potentials | 6 |
Change of Variables 1 Canonical Forms | 15 |
Copyright | |
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Common terms and phrases
1-parameter 2-dimensional a₁ bifurcation set canonical form catastrophe germ Catastrophe Theory Chapter coefficients components computed control parameter space critical manifold critical values cusp catastrophe degenerate critical point Delay Convention depends derivatives described determined diagrammatic dynamical system eigenvalues Elementary Catastrophe Theory equations of motion equilibrium Example extensive variables F₁ family of functions Figure fold catastrophe gradient system Hopf bifurcation imperfection sensitivity intersect isolated critical points linear local minimum Maxwell Convention Maxwell set metric tensor minima minimum monomials Morse functions neighborhood non-Morse critical point nonlinear occur open regions open sets parameterized perturbation phase portrait physical plane potential V(x qualitative properties representation saddle scale separatrix shown in Fig solution stability matrix structurally stable susceptibility tensor symmetry tangent space Taylor series Taylor series expansion terms of degree thermodynamic variables transformation unstable V₁ variance x²y zero