Titlebook: Bifurcations and Catastrophes; Geometry of Solution Michel Demazure Textbook 2000 Springer-Verlag Berlin Heidelberg 2000 Bifurcations.Catas

肉身

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

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

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

十字架

hardheaded

Interlocking

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

横条

Embolic-Stroke

https://doi.org/10.1007/978-3-642-57134-3Bifurcations; Catastrophes; Dynamical Systems; Maxima; Nonlinear; Singularities; catastrophe theory; diffeo