Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Math HOME

.......................

Faculty

.......................

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

Books

  1. Petters, A, Algebra, Geometry, and Trignonometry (2007), BRC Publishing
  2. A.O. Petters, Algebra, Geometry, and Trigonometry: Student and Teacher Editions (August, 2007), BRC, Benque-Belize
  3. Petters, AO; Dong, X, An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition (June, 2016), pp. 483 pages, SPRINGER, ISBN 1493937812  [abs]
  4. A. O. Petters and X. Dong, An Introduction to Mathematical Finance: Understanding and Building Financial Intuition, SUMAT (Winter, 2016), Springer, in preparation
  5. Kayser, R; Schramm, T; Nieser, L, Gravitational lenses proceedings of a conference held in Hamburg, Germany, 9-13 September 1991 (1992), pp. 399 pages, Springer-Verlag
  6. A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes (Spring, 2017), Springer, in preparation
  7. Petters, A, PSE Mathematics (2007), BRC Publishing
  8. A.O. Petters, PSE Mathematics: Student and Teacher Editions (February, 2007), BRC, Benque-Belize
  9. Petters, A, Scientific Reasoning (2007), BRC Publishing
  10. A.O. Petters, Scientific Reasoning: Student and Teacher Editions (July, 2007), BRC, Benque-Belize
  11. Petters, AO; Levine, H; Wambsganss, J, Singularity Theory and Gravitational Lensing, Progress in Mathematical Physics, Volume 21 (June, 2001), pp. 603 pages, Springer Science & Business Media, ISBN 0817636684 [002-1045375-379126]  [abs]

Papers Published

  1. Petters, AO, A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing, Symposium International Astronomical Union, vol. 173 no. 173 (1996), pp. 281-282, Cambridge University Press (CUP), ISSN 0074-1809 [Gateway.cgi], [doi]  [abs]
  2. Petters, AO; Rider, B; Teguia, AM, A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps, Journal of Mathematical Physics, vol. 50 no. 7 (August, 2009), pp. 072503-072503, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  3. Petters, AO; Rider, B; Teguia, AM, A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula, Journal of Mathematical Physics, vol. 50 no. 12 (December, 2009), pp. 122501-122501, AIP Publishing, ISSN 0022-2488 [repository], [doi]  [abs]
  4. Aazami, AB; Petters, AO, A universal magnification theorem for higher-order caustic singularities, Journal of Mathematical Physics, vol. 50 no. 3 (Spring, 2009), pp. 032501-032501, AIP Publishing, ISSN 0022-2488 [3447], [doi]  [abs]
  5. Aazami, AB; Petters, AO, A universal magnification theorem. II. Generic caustics up to codimension five, Journal of Mathematical Physics, vol. 50 no. 8 (September, 2009), pp. 023503, ISSN 0022-2488 [repository], [doi]  [abs]
  6. Aazami, AB; Petters, AO, A universal magnification theorem. III. Caustics beyond codimension 5, Journal of Mathematical Physics, vol. 51 no. 2 (Summer, 2010), pp. 082501, ISSN 0022-2488 [doi]  [abs]
  7. 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)
  8. Levine, H; Petters, AO; Wambsganss, J, Applications of Singularity Theory to Gravitational Lensing, J. Math. Phys., vol. 34 no. 10 (1993), pp. 4781, ISSN 0022-2488  [abs]
  9. Levine, HI; Petters, AO; Wambsganss, J, Applications of singularity theory to gravitational lensing. I. Multiple lens planes, Journal of Mathematical Physics, vol. 34 no. 10 (January, 1993), pp. 4781-4808, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  10. Petters, AO, Arnold's singularity theory and gravitational lensing, Journal of Mathematical Physics, vol. 34 no. 8 (January, 1993), pp. 3555-3581, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  11. Petters, AO; Witt, HJ, Bounds on number of cusps due to point mass gravitational lenses, Journal of Mathematical Physics, vol. 37 no. 6 (June, 1996), pp. 2920-2933, AIP Publishing [doi]  [abs]
  12. Petters, AO; Witt, H, Bounds on Number of Cusps Due to Point Mass Gravitional Lenses with Continuous Matter and Shear, J. Math. Phys., vol. 37 no. 2920 (1996), pp. 2920-2933 [doi]  [abs]
  13. Petters, AO; Wicklin, FJ, Caustics of the double-plane two-point-mass gravitational lens with continuous matter and shear, Monthly Notices of the Royal Astronomical Society, vol. 277 no. 4 (Summer, 1995), pp. 1399-1403, Oxford University Press (OUP), ISSN 0035-8711 [Gateway.cgi], [doi]
  14. GAUDI, BS; PETTERS, AO, CENTER OF LIGHT CURVES FOR WHITNEY FOLD AND CUSP (December, 2002), pp. 2103-2104, World Scientific Publishing Company [doi]
  15. 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)
  16. Petters, AO, Curvature of caustics and singularities of gravitational lenses, Nonlinear Analysis: Theory, Methods & Applications, vol. 30 no. 1 (January, 1997), pp. 627-634, Elsevier BV, ISSN 0362-546X [doi]
  17. Petters, AO; Wicklin, FJ, Fixed points due to gravitational lenses, Journal of Mathematical Physics, vol. 39 no. 2 (January, 1998), pp. 1011-1023, AIP Publishing [doi]  [abs]
  18. Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects. II. Probing post-post-Newtonian metrics, Physical Review D, vol. 73 no. 4 (March, 2006), pp. 044024, American Physical Society (APS), ISSN 1550-7998 [0601053], [doi]  [abs]
  19. Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects. III. Braneworld gravity, Physical Review D, vol. 73 no. 10 (May, 2006), pp. 104032, American Physical Society (APS), ISSN 1550-7998 [0603061], [doi]  [abs]
  20. Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects: Static, spherically symmetric case, Physical Review D, vol. 72 no. 10 (November, 2005), pp. 104006, American Physical Society (APS), ISSN 1550-7998 [0511019], [doi]  [abs]
  21. Gaudi, BS; Petters, AO, Gravitational microlensing near caustics. I. Folds, The Astrophysical Journal, vol. 574 no. 2 I (August, 2002), pp. 970-984, IOP Publishing, ISSN 0004-637X [0112531], [doi]  [abs]
  22. Gaudi, BS; Petters, AO, Gravitational microlensing near caustics. II. Cusps, The Astrophysical Journal, vol. 580 no. 1 I (November, 2002), pp. 468-489, IOP Publishing, ISSN 0004-637X [0206162v2], [doi]  [abs]
  23. Petters, AO, Gravity's action on light, Notices of the American Mathematical Society, vol. 57 no. 11 (December, 2010), pp. 1392-1409, ISSN 0002-9920
  24. Keeton, CR; Gaudi, BS; Petters, AO, Identifying lenses with small-scale structure. I. Cusp lenses, The Astrophysical Journal, vol. 598 no. 1 I (November, 2003), pp. 138-161, IOP Publishing, ISSN 0004-637X [doi]  [abs]
  25. Keeton, CR; Gaudi, BS; Petters, AO, Identifying lenses with small-scale structure. II. Fold lenses, The Astrophysical Journal, vol. 635 no. 1 I (December, 2005), pp. 35-59, IOP Publishing, ISSN 0004-637X [doi]  [abs]
  26. Keeton, C; Gaudi, S; Petters, AO, Identifying Lensing by Small-Scale Structure. II. Fold Lenses, Astrophysical Journal, vol. 635 no. 1 I (November, 2005), pp. 35-35, ISSN 0004-637X [0503452], [doi]  [abs]
  27. Keeton, C; Gaudi, S; Petters, AO, Identifying Lensing by Substructure I. Cusp Lenses, Astrophys. J., vol. 598 no. 1 I (2003), pp. 138, ISSN 0004-637X [0210318], [doi]  [abs]
  28. Aazami, AB; Keeton, CR; Petters, AO, Lensing by Kerr black holes. I. General lens equation and magnification formula, Journal of Mathematical Physics, vol. 52 no. 9 (September, 2011), pp. 092502-092502, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  29. Aazami, AB; Keeton, CR; Petters, AO, Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables, Journal of Mathematical Physics, vol. 52 no. 10 (October, 2011), pp. 102501-102501, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  30. Iyer, SV; Petters, AO, Light's bending angle due to black holes: From the photon sphere to infinity, General Relativity and Gravitation, vol. 39 no. 10 (October, 2007), pp. 1563-1582, Springer Nature, ISSN 0001-7701 [0611086], [doi]  [abs]
  31. Fetters, AO, Lower bounds on image magnification in gravitational lensing, Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 452 no. 1949 (January, 1996), pp. 1475-1490, The Royal Society, ISSN 1364-5021 [doi]  [abs]
  32. Aazami, AB; Keeton, CR; Petters, AO, Magnification cross sections for the elliptic umbilic caustic surface, Universe, vol. 5 no. 7 (July, 2019) [doi]  [abs]
  33. Werner, MC; Petters, AO, Magnification relations for Kerr lensing and testing cosmic censorship, Physical Review D, vol. 76 no. 6 (September, 2007), pp. 064024, American Physical Society (APS), ISSN 1550-7998 [0132], [doi]  [abs]
  34. 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)
  35. Petters, AO; Werner, MC, Mathematics of gravitational lensing: Multiple imaging and magnification, General Relativity and Gravitation, vol. 42 no. 9 (Fall, 2010), pp. 2011-2046, Springer Nature, ISSN 0001-7701 [doi]  [abs]
  36. 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)
  37. Petters, AO, Morse theory and gravitational microlensing, Journal of Mathematical Physics, vol. 33 no. 5 (January, 1992), pp. 1915-1931, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  38. Petters, AO, Multiplane gravitational lensing. I. Morse theory and image counting, Journal of Mathematical Physics, vol. 36 no. 8 (January, 1995), pp. 4263-4275, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  39. Petters, AO, Multiplane gravitational lensing. II. Global geometry of caustics, Journal of Mathematical Physics, vol. 36 no. 8 (January, 1995), pp. 4276-4295, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  40. Petters, AO, Multiplane gravitational lensing. III. Upper bound on number of images, Journal of Mathematical Physics, vol. 38 no. 3 (January, 1997), pp. 1605-1613, AIP Publishing [doi]  [abs]
  41. Petters, AO; Wicklin, FJ, New Caustic Phenomena In Double-Plane Lensing, Symposium International Astronomical Union, vol. 173 (1996), pp. 283-284, Cambridge University Press (CUP) [doi]  [abs]
  42. Levine, H; Petters, AO, New Caustic Singularities in Multiple Lens Plane Gravitational Lensing, Astron. Astrophys., vol. 272 no. L17 (1993), pp. L17-L19, EDP SCIENCES S A
  43. Petters, AO, On relativistic corrections to microlensing effects: Applications to the Galactic black hole, Monthly Notices of the Royal Astronomical Society, vol. 338 no. 2 (January, 2003), pp. 457-464, Oxford University Press (OUP) [0208500], [doi]  [abs]
  44. Aazami, AB; Petters, AO; Rabin, JM, Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing, Journal of Mathematical Physics, vol. 52 no. 2 (February, 2011), pp. 022501-022501, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  45. 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)
  46. 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)
  47. Witt, HJ; Petters, AO, Singularities of the one- and two-point mass gravitational lens, Journal of Mathematical Physics, vol. 34 no. 9 (January, 1993), pp. 4093-4111, AIP Publishing, ISSN 0022-2488 [doi]  [abs]
  48. 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)
  49. 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
  50. 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)
  51. Keeton, CR; Petters, AO, Testing theories of gravity with black hole lensing, 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories Proc. of the Mg11 Meeting on General Relativity (January, 2008), pp. 1719-1721 [doi]  [abs]
  52. 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
  53. Frittelli, S; Petters, AO, Wavefronts, caustic sheets, and caustic surfing in gravitational lensing, Journal of Mathematical Physics, vol. 43 no. 11 (November, 2002), pp. 5578-5611, AIP Publishing, ISSN 0022-2488 [0208135], [doi]  [abs]

Other

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

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
Mathematics Home | Arts & Sciences | Duke University