Publications of Arlie O Petters     :recent first  combined  bibtex listing:

Books

1. A. O. Petters, H. Levine, and J. Wambsganss, Singularity Theory and Gravitational Lensing, Progress in Mathematical Physics, Volume 21 (June, 2001), Birkhauser [002-1045375-379126]
2. A.O. Petters, PSE Mathematics: Student and Teacher Editions (February, 2007), BRC, Benque-Belize
3. A.O. Petters, Scientific Reasoning: Student and Teacher Editions (July, 2007), BRC, Benque-Belize
4. A.O. Petters, Algebra, Geometry, and Trigonometry: Student and Teacher Editions (August, 2007), BRC, Benque-Belize
5. X. Dong and A.O. Petters, Mathematical Finance I (June, 2009), in preparation
6. X. Dong and A. O. Petters, Mathematical Finance II (June, 2009), in preparation
7. A. O. Petters, Gravitational Lensing and Black Holes (August, 2009), in preparation

Papers Published

1. A. O. Petters, Morse Theory and Gravitational Microlensing, J. Math. Phys., vol. 33 (1992), pp. 1915
2. A. O. Petters and D. Spergel, An Analytical Approach to Quasar Variability due to Microlensing, Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics, 406, Springer, Ber1in) (1992)
3. A. O. Petters, Morse Theory and Gravitational Microlensing, Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Ber1in) (1992)
4. H. Levine, A. O. Petters, and J. Wambsganss, Applications of Singularity Theory to Gravitational Lensing, J. Math. Phys., vol. 34 (1993), pp. 4781
5. H. Witt and A. O. Petters, Singularities of the One and Two Point Mass Gravitational Lens, J. Math. Phys., 34, 4781 (1993)
6. H. Levine and A. O. Petters, New Caustic Singularities in Multiple Lens Plane Gravitational Lensing, Astron. Astrophys., vol. 272 no. L17 (1993)
7. A. O. Petters, Arnold's Singularity Theory and Gravitational Lensing, J. Math. Phys., vol. 34 (1993), pp. 3555
8. H. Levine and A. O. Petters, Singularities and Gravitational Lensing, Passion des Formes: Hommage a Rene Thom,Vol. 1 (M. Porte, ed.) E.N.S. Edition, Fontenany-St Cloud (1994)
9. A. O. Petters, Multiplane Gravitational Lensing I: Morse Theory and Image Counting, J. Math. Phys., vol. 36 (March, 1995), pp. 4263
10. A. O. Petters, Multiplane Gravitational Lensing II: Global Geometry of Caustics, J. Math. Phys., vol. 36 (April, 1995), pp. 4276
11. A. O. Petters, F.J. Wicklin, Caustics of the Double-Plane Two Point-Mass Gravitational Lens with Continuous Matter and Shear, Mon. Not. R. Astron. Soc., vol. 277 (Summer, 1995), pp. 1399
12. A. O. Petters, Lower Bounds on Image Magnification in Gravitational Lensing, Proc. R. Soc. Lond. A, vol. 452 (1996), pp. 1475
13. A. O. Petters, A Cusp-Counting Formula for Caustics Due to Multiplane Gravitational Lensing, Astrophysical Applications of Gravitational Lensing, eds. C.S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht) (1996)
14. A. O. Petters, Mathematical Aspects of Gravitational Lensing, Proceedings of the Seventh Marcel Grossman Meeting on General Relativity, Vol. B, eds. R.T. Jantzen and G.M. Keiser (World Scientific, Singapore) (1996)
15. A. O. Petters and F.J. Wicklin, New Caustic Phenomena for Caustics in Double-Plane Lensing, Astrophysical Applications of Gravitational Lensing, eds. C.S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht) (1996)
16. A. O. Petters and H. Witt, Bounds on Number of Cusps Due to Point Mass Gravitional Lenses with Continuous Matter and Shear, J. Math. Phys., vol. 37 no. 2920 (1996)
17. A. O. Petters, Curvature of Caustics and Singularities of Gravitational Lenses, Proceedings of the Second World Congress of Nonlinear Analysts ed. V. Lakshmikantham (Elsevier Science Ltd., Oxford) (1997)
18. A. O. Petters, Multiplane Gravitational Lensing III. Upper Bound on Number of Images, J. Math. Phys., vol. 38 (1997), pp. 1605
19. A. O. Petters, F.J. Wicklin, Counting Formulas and Bounds on Number of Fixed Points Due to Point-Mass Lenses, Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity 1997, ed. R. Ruffini (World Scientific, Singapore) (Summer, 1997)
20. S. Mao, A. O. Petters, and H. Witt, Properties of Point Mass Lenses on a Regular Polygon and the Problem of Maximum Number of Lensed Images, in Proceedings of the Eighth Marcel Grossman Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore) (Summer, 1997)
21. A. O. Petters, Some Global Results on Gravitational Lensing, Proceedings of the Eight Marcel Grossman Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore) (Summer, 1997)
22. A. O. Petters, F. Wicklin, Fixed Points Due to Gravitational Lenses, J. Math. Phys., 39, 1011 (1998)
23. A. O. Petters, Stable Lens Systems, Lensed Image Magnification,and Magnification Cross Sections, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (2001), World Scientific, Singapore
24. S. Frittelli and A. O. Petters, Wavefront Singularities due to an Elliptical Potential, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (2001), World Scientific, Singapore
25. B. S. Gaudi and A. O. Petters, Center of Light Curves for Whitney Fold and Cusp, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific,Singapore) (2001)
26. S. Gaudi and A. O. Petters, Gravitational Microlensing Near Caustics I: Folds, The Astrophysical Journal, 574, 970 (2002), vol. 574 no. 970 (2002) [0112531]
27. S. Gaudi and A. O. Petters, Gravitational Microlensing Near Caustics II: Cusps, The Astrophysical Journal, vol. 580 no. 468 (2002) [0206162]
28. S. Frittelli and A. O. Petters, Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing, J. Math. Phys., vol. 43 (2002), pp. 5578 [0208135]
29. A. O. Petters, On Relativistic Corrections to Microlensing Effects: Applications to the Galactic Black Hole, Monthly Notices of the Royal Astronomical Society, vol. 338 (2003), pp. 457 [0208500]
30. C. Keeton, S. Gaudi, and A.O. Petters, Identifying Lensing by Substructure I. Cusp Lenses, Astrophys. J., vol. 598 (2003), pp. 138 [0210318]
31. C. Keeton, S. Gaudi, and A.O. Petters, Identifying Lensing by Substructure II. Fold Lenses, Astrophysical Journal, vol. 635 (2005), pp. 35 [0503452]
32. C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I. Static, Spherically Symmetric Case, Physical Review D, vol. 72 (2005), pp. 104006 [0511019]
33. C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. II. Probing Post-Post-Newtonian Metrics, Phys. Rev. D, vol. 73 (2006), pp. 044024 [0601053]
34. C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. III. Braneworld Gravity, Phys. Rev. D, vol. 73 (2006), pp. 104032 [0603061]
35. C. Keeton and A.O. Petters, Testing Theories of Gravity with Black Hole Lensing, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (Summer, 2006)
36. S. Iyer and A.O. Petters, Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity, General Relativity and Gravitation, vol. 39 (2007), pp. 1563 [0611086]
37. M. C. Werner and A.O. Petters, Magnification Relations for Kerr Lensing and Testing Cosmic Censorship, Physical Review D, vol. 76 (September, 2007), pp. 064024 [0132]
38. A. M. Aazami and A.O. Petters, A Universal Magnification Theorem for Higher-Order Caustic Singularities, J. Math. Phys., vol. 50 (2009), pp. 032501 [3447]

Papers Submitted

1. A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps (2008)
2. A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula (2008)
3. A. B. Aazami and A.O. Petters, A Universal Magnification Theorem II. Generic Caustics up to Codimension Five (2009)

Other

1. A.O. Petters, Singularities in Gravitational Microlensing, Ph.D. Thesis, MIT, Department of Mathematics (1991)