Professor Arlie O. Petters

Benjamin Powell Professor


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 Publications:

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

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

  2. 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).

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

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

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


    BOOKS IN PREPARATION

  5. Gravitational Lensing and Black Holes
    A. O. Petters (Springer, New York, 2009). In preparation.
  6. Mathematical Finance with Applications
    X. Dong and A. O. Petters (2009). In preparation.



    PAPERS

  7. A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
    A. O. Petters, B. Rider, and A. M. Teguia, to appear in JMP (2009); astro-ph arXiv:0807.4984v2
  8. 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
  9. A Universal Magnification Theorem III. Caustics Beyond Codimension Five
    A. B. Aazami and A. O. Petters, to appear in JMP (2009); math-ph arXiv:0909.5235
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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).
  15. 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
  16. 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
  17. 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.
  18. 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.
  19. 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
  20. 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
  21. Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing
    S. Frittelli and A. O. Petters, J. Math. Phys., 43, 5578 (2002); astro-ph/0208135
  22. Gravitational Microlensing Near Caustics II: Cusps
    B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002); astro-ph/0206162
  23. Gravitational Microlensing Near Caustics I: Folds
    B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); astro-ph/0112531
  24. 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).
  25. 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).
  26. 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).
  27. Fixed Points due to Gravitational Lenses
    A.O. Petters and F.J. Wicklin, J. Math. Phys., 39, 1011 (1998).
  28. 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).
  29. 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.
  30. 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).
  31. 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).
  32. Multiplane Gravitational Lensing III. Upper Bound on Number of Images
    A. O. Petters, J. Math. Phys., 38, 1605 (1997).
  33. Lower Bounds on Image Magnification in Gravitational Lensing
    A. O. Petters, Proc. R. Soc. Lond. A, 452, 1475 (1996).
  34. A Cusp-Counting Formula for Caustics due to Multiplane Gravitational Lensing
    A. O. Petters, in Astrophysical Applications of Gravitational Lensing , ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  35. 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).
  36. New Caustic Phenomena for Caustics in Double-Plane Lensing
    A. O. Petters and F.J. Wicklin, in Astrophysical Applications of Gravitational Lensing , ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  37. 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).
  38. 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).
  39. Multiplane Gravitational Lensing II: Global Geometry of Caustics
    A. O. Petters, J. Math. Phys., 36, 4276 (1995).
  40. Multiplane Gravitational Lensing I: Morse Theory and Image Counting
    A. O. Petters, J. Math. Phys., 36, 4263 (1995).
  41. 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).
  42. Applications of Singularity Theory to Gravitational Lensing
    H. Levine, A. O. Petters, and J. Wambsganss, J. Math. Phys., 34, 4781 (1993).
  43. Singularities of the One and Two Point Mass Gravitational Lens
    H. Witt and A. O. Petters, J. Math. Phys., 34, 4093 (1993).
  44. New Caustic Singularities in Multiple Lens Plane Gravitational Lensing
    H. Levine and A. O. Petters, Astron. Astrophys., 272, L17 (1993).
  45. Arnold's Singularity Theory and Gravitational Lensing
    A. O. Petters, J. Math. Phys., 34, 3555 (1993).
  46. Morse Theory and Gravitational Microlensing
    A. O. Petters, J. Math. Phys., 33, 1915 (1992).
  47. 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).
  48. 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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