ARLIE O. PETTERS

PUBLICATIONS



    BOOKS

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

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

  2. Algebra, Geometry, and Trigonometry: Teacher Edition
    A. O. Petters (BRC, Benque-Belize, 2007). About the Book

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

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

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

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


    BOOKS IN PREPARATION

  5. Gravitational Lensing by Black Holes
    A. O. Petters (Birkhäuser-Springer, New York, 2008). In preparation.
  6. Mathematical Finance I
    X. Dong and A. O. Petters (2008). In preparation.
  7. Mathematical Finance II
    X. Dong and A. O. Petters (2008). In preparation.



    PAPERS

  8. A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps
    A. O. Petters, B. Rider, and A. M. Teguia (2008); astro-ph arXiv:0807.0232v1
  9. 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
  10. 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
  11. 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, eds. R. Ruffini (World Scientific, Singapore, 2006).
  12. 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
  13. 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
  14. 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 .
  15. 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 .
  16. 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 .
  17. 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 .
  18. Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing
    S. Frittelli and A. O. Petters, J. Math. Phys., 43, 5578 (2002); astro-ph/0208135 .
  19. Gravitational Microlensing Near Caustics II: Cusps
    B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002); astro-ph/0206162 .
  20. Gravitational Microlensing Near Caustics I: Folds
    B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); astro-ph/0112531 .
  21. 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).
  22. 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).
  23. 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).
  24. Fixed Points due to Gravitational Lenses
    A.O. Petters and F.J. Wicklin, J. Math. Phys., 39, 1011 (1998).
  25. 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).
  26. 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 .
  27. 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).
  28. Multiplane Gravitational Lensing III. Upper Bound on Number of Images
    A. O. Petters, J. Math. Phys., 38, 1605 (1997).
  29. 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).
  30. 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).
  31. 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).
  32. 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).
  33. 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).
  34. Lower Bounds on Image Magnification in Gravitational Lensing
    A. O. Petters, Proc. R. Soc. Lond. A, 452, 1475 (1996).
  35. 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).
  36. Multiplane Gravitational Lensing II: Global Geometry of Caustics
    A. O. Petters, J. Math. Phys., 36, 4276 (1995).
  37. Multiplane Gravitational Lensing I: Morse Theory and Image Counting
    A. O. Petters, J. Math. Phys., 36, 4263 (1995).
  38. 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).
  39. Applications of Singularity Theory to Gravitational Lensing
    H. Levine, A. O. Petters, and J. Wambsganss, J. Math. Phys., 34, 4781 (1993).
  40. Singularities of the One and Two Point Mass Gravitational Lens
    H. Witt and A. O. Petters, J. Math. Phys., 34, 4093 (1993).
  41. New Caustic Singularities in Multiple Lens Plane Gravitational Lensing
    H. Levine and A. O. Petters, Astron. Astrophys., 272, L17 (1993).
  42. Arnold's Singularity Theory and Gravitational Lensing
    A. O. Petters, J. Math. Phys., 34, 3555 (1993).
  43. Morse Theory and Gravitational Microlensing
    A. O. Petters, J. Math. Phys., 33, 1915 (1992).
  44. 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).
  45. 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).