Titlebook: Catastrophe Theory; Vladimir I. Arnold Book 1992Latest edition Springer-Verlag Berlin Heidelberg 1992 Bifurcations.Catastrophe Theory.Kata

jovial

https://doi.org/10.1007/978-3-031-46906-0In contrast to the example given above, the application of singularity theory to the study of bifurcations of equilibrium states in the theory of elasticity is irreproachably founded.

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兩棲動物

Markov Chain Monte Carlo MethodsLoss of stability of an equilibrium state on change of parameter is not necessarily associated with the bifurcation of this equilibrium state: it can lose stability not only by colliding with another state, but also by itself.

侵略主義

沉思的魚

János Abonyi,László Nagy,Tamás RuppertA . in phase space is defined as follows: at every point of the space we have not just one velocity vector (as in the usual evolutionary system), but a whole set of vectors called the ..

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János Abonyi,László Nagy,Tamás RuppertA smooth curve on the plane can have a tangent which touches it tangentially at any number of points, but this is not true for generic curves. By a small perturbation of the curve one can always achieve that no straight line will be tangential at more than two points.

上腭

Aleksandr Lobanov,Alexander GasnikovMathematicians know well that going over to the complex case usually simplifies a problem, rather than making it more complicated. For example, every algebraic equation of degree . has exactly . complex roots, while it is a difficult problem to find the number of real roots.

Gourmet

,Whitney’s Singularity Theory,In 1955 the American mathematician Hassler Whitney published the article ‘Mappings of the plane into the plane‘, laying the foundations for a new mathematical theory - the theory of singularities of smooth mappings.

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A Catastrophe Machine,In contrast to the example given above, the application of singularity theory to the study of bifurcations of equilibrium states in the theory of elasticity is irreproachably founded.

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Bifurcations of Equilibrium States,An . is described mathematically by a vector field in phase space. A point of phase space defines the . of the system. The vector at this point indicates the velocity of change of the state.