Titlebook: Singularity Theory and Gravitational Lensing; Arlie O. Petters,Harold Levine,Joachim Wambsganss Book 2001 Birkh?user Boston 2001 Mathemati

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Physical Applicationsortant applications, ranging from studies in the solar system, to galactic structure, to probing cosmological objects. Some of the practical consequences in lensing have been known for a long time and have been predicted early on, whereas other applications popped up only recently. In fact, gravitat

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Classification and Genericity of Stable Lens Systemsideally be expressed using maps resistant to small perturbations. This begs investigating the classification and gener-icity of stable lens systems. The problem then carries over to the time delay families, including the induced time delay functions and lensing maps, used to model gravitational lens

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Local Lensing Geometrye qualitative features of .plane lensing maps near fold and cusp critical points, including quantitative results for the single and double-plane cases. This is followed by a study of the local geometry of caustics under 1-parameter evolutions. These results bear on Problem ., which includes a charac

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Morse Inequalities inequalities called the .. We shall see in subsequent chapters that the Morse inequalities impact powerfully on several central issues in gravitational lensing: counting lensed images (Chapters 11 and 12), finding lower bounds on total magnification (Chapter 13), and linking the total curvature of

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Counting Lensed Images: Single-Plane Casea light source at position . are solutions . of the lens equation (see (6.30) on page 200 and Section 3.2.3, page 77):.where . is the bending angle vector field on the .th lens plane and . the .th partial lensing map. For a gravitational lens consisting of a single point mass (e.g., star or black ho