Professor Arlie O. Petters

Benjamin Powell Professor

 Publications:

BOOKS
  1. An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition
    A. O. Petters and X. Dong (Springer, SUMAT Series, New York, 2016)

    Solutions Manual for Students: An Introduction to Mathematical Finance with Applications
    A. O. Petters and X. Dong (Springer, New York, 2017)

    Solutions Manual for Instructors Only: An Introduction to Mathematical Finance with Applications
    A. O. Petters and X. Dong (Springer, New York, 2017)

  2. Scientific Reasoning: Teacher Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

    Scientific Reasoning: Student Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

  3. Algebra, Geometry, and Trigonometry: Teacher Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

    Algebra, Geometry, and Trigonometry: Student Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

  4. PSE Mathematics: Teacher-Tutor-Parent Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

    PSE Mathematics: Student Edition
    A. O. Petters (BRC, Benque-Belize, 2007)

  5. Singularity Theory and Gravitational Lensing
    A. O. Petters, H. Levine, and J. Wambsganss (Birkhäuser-Springer, Boston, 2001)


    BOOK IN PREPARATION

  6. Gravitational Lensing and Black Holes
    M. C. Werner and A. O. Petters (Springer, New York, 2018). In preparation.



    PAPERS

  7. Lensing by Kerr Black Holes. II. Analytical Study of Quasi-Equatorial Lensing Observables
    A. B. Aazami, C. R. Keeton, and A. O. Petters, J. Math. Phys. 52, 102501 (2011); astro-ph arXiv:1002.4304v1.
  8. Lensing by Kerr Black Holes. I. General Lens Equation and Magnification Formula
    A. B. Aazami, C. R. Keeton, and A. O. Petters, J. Math. Phys. 52, 092502 (2011); astro-ph arXiv:1102.4300v1.
  9. Orbifolds, the A, D, E Caustic Singularities, and Gravitational Lensing
    A. B. Aazami, A. O. Petters, and J. M. Rabin, J. Math. Phys. 51, 022501 (2011); math-ph arXiv:1004.0516v1.
  10. Gravity's Action on Light
    A. O. Petters, Notices of the AMS 57, 1392 (2010).
  11. Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
    A. O. Petters and M. C. Werner, Gen. Rel. and Grav., Special Issue on Gravitational Lensing (2010); astro-ph arXiv:0912.0490v1.
  12. A Universal Magnification Theorem. III. Caustics Beyond Codimension Five
    A. B. Aazami and A. O. Petters, J. Math. Phys. 51, 023503 (2010); math-ph arXiv:0909.5235.
  13. A Mathematical Theory of Stochastic Microlensing. II. Random Images, Shear, and the Kac-Rice Formula
    A. O. Petters, B. Rider, and A. M. Teguia, J. Math. Phys. 50,122501 (2009); astro-ph arXiv:0807.4984v2.
  14. A Mathematical Theory of Stochastic Microlensing. I. Random Time Delay Functions and Lensing Maps
    A. O. Petters, B. Rider, and A. M. Teguia, J. Math. Phys. 50, 072503 (2009); astro-ph arXiv:0807.0232v2.
  15. A Universal Magnification Theorem II. Generic Caustics up to Codimension Five
    A. B. Aazami and A. O. Petters, J. Math. Phys. 50, 082501 (2009); math-ph arXiv:0904.2236v4.
  16. A Universal Magnification Theorem for Higher-Order Caustic Singularities
    A. B. Aazami and A. O. Petters, J. Math. Phys. 50, 032501 (2009); astro-ph arXiv:0811.3447v2.
  17. Magnification Relations for Kerr Lensing and Testing Cosmic Censorship
    M. C. Werner and A. O. Petters, Phys. Rev. D 76, 064024 (2007); gr-qc/0706.0132.
  18. Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity
    S. V. Iyer and A. O. Petters, Gen. Rel. and Grav. 39, 1563 (2007); gr-qc/0611086.
  19. Testing Theories of Gravity with Black Hole Lensing C. Keeton and A. O. Petters, in Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 2006).
  20. Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. III. Braneworld Gravity
    C. Keeton and A. O. Petters, Phys. Rev. D 73, 104032 (2006) gr-qc/0603061.
  21. Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. II. Probing Post-Post-Newtonian Metrics
    C. Keeton and A. O. Petters, Phys. Rev. D 73, 044024 (2006); gr-qc/0601053.
  22. Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I. Static, Spherically Symmetric Case
    C. Keeton and A. O. Petters, Phys. Rev. D, 72, 104006 (2005); gr-qc/0511019.
  23. Identifying Lenses with Small-Scale Structure. II. Fold Lenses
    C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 635, 35 (2005); astro-ph/0503452.
  24. Identifying Lenses with Small-Scale Structure. I. Cusp Lenses
    C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 598, 138 (2003); astro-ph/0210318.
  25. On Relativistic Corrections to Microlensing Effects: Applications to the Galactic Black Hole
    A. O. Petters, Mon. Not. R. Astron. Soc., 338, 457 (2003); astro-ph/0208500.
  26. Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing
    S. Frittelli and A. O. Petters, J. Math. Phys., 43, 5578 (2002); astro-ph/0208135.
  27. Gravitational Microlensing Near Caustics. II: Cusps
    B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002); astro-ph/0206162.
  28. Gravitational Microlensing Near Caustics. I: Folds
    B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); astro-ph/0112531.
  29. Stable Lens Systems, Lensed Image Magnification, and Magnification Cross Sections
    A. O. Petters, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  30. Wavefront Singularities due to an Elliptical Potential
    S. Frittelli and A. O. Petters, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  31. Center of Light Curves for Whitney Fold and Cusp
    B. S. Gaudi and A. O. Petters, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  32. Fixed Points due to Gravitational Lenses
    A.O. Petters and F.J. Wicklin, J. Math. Phys., 39, 1011 (1998).
  33. Counting Formulas and Bounds on Number of Fixed Points due to Point-Mass Lenses
    A. O. Petters and F.J. Wicklin, in Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 1997).
  34. Properties of Point Mass Lenses on a Regular Polygon and the Problem of Maximum Number of Lensed Images
    S. Mao, A. O. Petters, and H. Witt, in Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 1997); astro-ph/0708111.
  35. Some Global Results on Gravitational Lensing
    A. O. Petters, in Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 1997).
  36. Curvature of Caustics and Singularities of Gravitational Lenses
    A. O. Petters, in Proceedings of the Second World Congress of Nonlinear Analysts, ed. V. Lakshmikantham (Elsevier Science Ltd., Oxford, 1997).
  37. Multiplane Gravitational Lensing III. Upper Bound on Number of Images
    A. O. Petters, J. Math. Phys., 38, 1605 (1997).
  38. Lower Bounds on Image Magnification in Gravitational Lensing
    A. O. Petters, Proc. R. Soc. Lond. A, 452, 1475 (1996).
  39. A Cusp-Counting Formula for Caustics due to Multiplane Gravitational Lensing
    A. O. Petters, in Astrophysical Applications of Gravitational Lensing, eds. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  40. Mathematical Aspects of Gravitational Lensing
    A. O. Petters, in Proceedings of the Seventh Marcel Grossmann Meeting on General Relativity, vol. B, eds. R. T. Jantzen and G. M. Keiser (World Scientific, Singapore, 1996).
  41. New Caustic Phenomena for Caustics in Double-Plane Lensing
    A. O. Petters and F.J. Wicklin, in Astrophysical Applications of Gravitational Lensing, eds. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  42. Bounds on Number of Cusps due to Point Mass Gravitational Lenses with Continuous Matter and Shear
    A. O. Petters and H. Witt, J. Math. Phys., 37, 2920 (1996).
  43. Caustics of the Double-Plane Two Point-Mass Gravitational Lens with Continuous Matter and Shear
    A. O. Petters and F.J. Wicklin, Mon. Not. R. Astron. Soc., 277, 1399 (1995).
  44. Multiplane Gravitational Lensing II: Global Geometry of Caustics
    A. O. Petters, J. Math. Phys., 36, 4276 (1995).
  45. Multiplane Gravitational Lensing I: Morse Theory and Image Counting
    A. O. Petters, J. Math. Phys., 36, 4263 (1995).
  46. Singularities and Gravitational Lensing
    H. Levine and A. O. Petters, in Passion des Formes: Hommage `a Rene' Thom , vol. 1, ed. M. Porte (E.N.S. Edition, Fontenay-St Cloud, 1994).
  47. Applications of Singularity Theory to Gravitational Lensing
    H. Levine, A. O. Petters, and J. Wambsganss, J. Math. Phys., 34, 4781 (1993).
  48. Singularities of the One and Two Point Mass Gravitational Lens
    H. Witt and A. O. Petters, J. Math. Phys., 34, 4093 (1993).
  49. New Caustic Singularities in Multiple Lens Plane Gravitational Lensing
    H. Levine and A. O. Petters, Astron. Astrophys., 272, L17 (1993).
  50. Arnold's Singularity Theory and Gravitational Lensing
    A. O. Petters, J. Math. Phys., 34, 3555 (1993).
  51. Morse Theory and Gravitational Microlensing
    A. O. Petters, J. Math. Phys., 33, 1915 (1992).
  52. An Analytical Approach to Quasar Variability due to Microlensing
    A. O. Petters and D. Spergel, in Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Berlin, 1992).
  53. Morse Theory and Gravitational Microlensing
    A. O. Petters, in Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Berlin, 1992).


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