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Catastrophe theory: Quiz


Question 1: eleven) generic structures for these bifurcation geometries, with corresponding standard forms into which the Taylor series around the catastrophe germs can be transformed by ________ (a smooth transformation whose inverse is also smooth).
Differentiable manifoldManifoldFiber bundleDiffeomorphism

Question 2: They are the only way we currently have of detecting ________ and the dark matter of the universe, via the phenomenon of gravitational lensing producing multiple images of distant quasars.
Schwarzschild metricKerr metricBlack holeKerr–Newman metric

Question 3: They can be observed in ________ in the focal surfaces created by light reflecting off a surface in three dimensions and are intimately connected with the geometry of nearly spherical surfaces.
OpticsAnti-reflective coatingTransparency and translucencyOptical fiber

Question 4: This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a ________.
SoilEarthquakeLandslideMass wasting

Question 5: The degeneracy of these critical points can be unfolded by expanding the potential function as a ________ in small perturbations of the parameters.
Taylor's theoremTaylor seriesSeries (mathematics)Trigonometric functions

Question 6: By repeatedly increasing b and then decreasing it, one can therefore observe ________ loops, as the system alternately follows one solution, jumps to the other, follows the other back, then jumps back to the first.
MagnetismElectricityMagnetic fieldHysteresis

Question 7: In mathematics, catastrophe theory is a branch of ________ in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Bifurcation diagramSaddle-node bifurcationBifurcation theoryDifferential equation

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