Titlebook: Structural Stability in Physics; Proceedings of Two I Werner Güttinger,Horst Eikemeier Conference proceedings 1979 Springer-Verlag Berlin H

薄荷醇

Semiclassical Path Integrals in Terms of CatastrophesUsing a splitting procedure for action functionals, a semiclassical approximation of path integrals, remaining finite on caustics, is constructed. It is governed by oscillatory generalized Airy integrals involving catastrophe polynomials, whose bifurcation properties reflect those of real and complex classical paths.

Reverie

Catastrophe and Stochasticity in Semiclassical Quantum MechanicsThe symposium talk was an account of material already published [1,2,3,4]. Therefore this contribution will be an extended summary, in the form of a series of assertions for which justification will be found in the papers cited.

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Springer Series in Synergeticshttp://image.papertrans.cn/t/image/880045.jpg

pessimism

https://doi.org/10.1007/978-3-642-67363-4catastrophe theory; diffraction; dynamical systems; fields; fold catastrophe; fractal; mechanics; phase dia

脆弱么

饮料

debase

剥皮

Optical Caustics and Diffraction Catastrophes The caustics formed by an irregular water drop lens are a good example. By allowing the shape of the drop to change under the control of one or more parameters catastrophes of higher codimension can be formed, in particular, the parabolic umbilic (D.) and the symbolic umbilic (E.). They correspond

增强

变化无常

Catastrophes and Bifurcations in Variational Problemsderiving from variational problems, are shown to be determined by those of the stationary points of unfoldings of singularities and so are classifiable in terms of catastrophe polynomials. A stability analysis of the bifurcating solutions is carried out. The results are applied to the buckling of co