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Perturbation of quadrics
Clotet Juan, Josep; Magret Planas, Maria dels Dolors; Puerta Coll, Xavier
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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
Dynamical systems
Global analysis (Mathematics)
quadric
versal deformation
bifurcation diagram
Equacions diferencials ordinàries
Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
Classificació AMS::34 Ordinary differential equations::34D Stability theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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