Mathematics – Mathematical Physics
Scientific paper
Feb 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jmp....39.1011p&link_type=abstract
Journal of Mathematical Physics, Vol. 39, No. 2, p. 1011 - 1023
Mathematics
Mathematical Physics
4
Gravitational Lenses
Scientific paper
A fixed point of a gravitational lensing map represents those positions from which a pointlike light source has a lensed image that, despite gravitational lensing, corresponds to the original position of the source. The authors study fixed points of lensing maps due to a generic gravitational lens with applications to nonsingular isolated lenses, and to point-mass lenses with continuous matter and shear. Counting formulas and bounds on the number of fixed points are determined. The results include an odd-number fixed-point theorem for nonsingular isolated deflectors. Information on the positions of fixed points are found for the case of point masses on a lens plane with and without shear. The methods of the paper are based on Morse theory, complex variables, and resultants.
Petters Arlie O.
Wicklin Frederick J.
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