肉身
发表于 2025-3-25 07:01:47
Classification of Differentiable Functions,. We follow the method suggested by the Transversality Theorem in going from ’generic’ situations to more particular ones. First of all, as the Local Inversion Theorem shows, for a generic function f at a generic point a there is nothing to say: such a function can be written as . where . is one mem
Lignans
发表于 2025-3-25 08:13:22
Catastrophe Theory, most common applications we are concerned with potentials depending on a finite sequence of control parameters and we study the bifurcation of their equilibrium states. For the reasons given in the Introduction, we are particularly interested in . families. Moreover, what we want to do essentially
indifferent
发表于 2025-3-25 15:12:22
Vector Fields,by differential equations. We start by associating to each state of the system a ’representative’ point, and the set of these points forms what in general we call the . of the system. This representation of the state of a system by a point in phase space must be rich enough so that knowing the point
Anterior
发表于 2025-3-25 18:29:35
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十字架
发表于 2025-3-25 21:11:09
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hardheaded
发表于 2025-3-26 02:59:23
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Interlocking
发表于 2025-3-26 04:46:19
Bifurcations of Phase Portraits, (as in Chapt. 5, we may talk about control parameters, hidden parameters, imperfection parameters, … ) and we wish to understand how the phase portrait changes as the parameters vary. This is the question answered by catastrophe theory when we restrict to dissipative systems governed by a potential
争吵
发表于 2025-3-26 09:48:01
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横条
发表于 2025-3-26 13:39:54
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Embolic-Stroke
发表于 2025-3-26 20:07:27
https://doi.org/10.1007/978-3-642-57134-3Bifurcations; Catastrophes; Dynamical Systems; Maxima; Nonlinear; Singularities; catastrophe theory; diffeo