Perturbation of quadrics
Copyright policy )Perturbation of quadrics
The aim of this paper is to study what happens when a slight perturbation affects the coefficients of a quadratic equation defining a variety (a quadric) in R^n. Structurally stable quadrics are those a small perturbation on the coefficients of the equation defining them does not give rise to a "different" (in some sense) set of points. In particular we characterize structurally stable quadrics and give the "bifurcation diagrams" of the non stable ones (showing which quadrics meet all of their neighbourhoods), when dealing with the "affine" and "metric" equivalence relations. This study can be applied to the case where a set of points which constitute the set of solutions of a problem is deffined by a quadratic equation whose coefficients are given with parameter uncertainty.
Differential equations, Versal deformation, Numerical Analysis, Algebra and Number Theory, quadric, Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory, bifurcation diagram, versal deformation, Perturbations of ordinary differential equations, Bifurcation diagram, Classificació AMS::34 Ordinary differential equations::34D Stability theory, Quadric, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, analysis on manifolds::58K Theory of singularities and catastrophe theory, Structural stability and analogous concepts of solutions to ordinary differential equations, Elementary problems in Euclidean geometries, Classificació AMS::58 Global analysis, Dynamical systems, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], Discrete Mathematics and Combinatorics, Geometry and Topology, Global analysis (Mathematics), Equacions diferencials ordinàries, :58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory [Classificació AMS], :34 Ordinary differential equations::34D Stability theory [Classificació AMS]
Differential equations, Versal deformation, Numerical Analysis, Algebra and Number Theory, quadric, Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory, bifurcation diagram, versal deformation, Perturbations of ordinary differential equations, Bifurcation diagram, Classificació AMS::34 Ordinary differential equations::34D Stability theory, Quadric, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, analysis on manifolds::58K Theory of singularities and catastrophe theory, Structural stability and analogous concepts of solutions to ordinary differential equations, Elementary problems in Euclidean geometries, Classificació AMS::58 Global analysis, Dynamical systems, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], Discrete Mathematics and Combinatorics, Geometry and Topology, Global analysis (Mathematics), Equacions diferencials ordinàries, :58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory [Classificació AMS], :34 Ordinary differential equations::34D Stability theory [Classificació AMS]
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