Publications of Arlie O Petters :chronological combined listing:
%% Books
@book{fds15387,
Author = {A. O. Petters},
Title = {Gravitational Lensing and Black Holes},
Publisher = {in preparation},
Year = {2009},
Month = {August},
Key = {fds15387}
}
@book{fds51036,
Author = {X. Dong and A. O. Petters},
Title = {Mathematical Finance II},
Publisher = {in preparation},
Year = {2009},
Month = {June},
Key = {fds51036}
}
@book{fds28898,
Author = {X. Dong and A.O. Petters},
Title = {Mathematical Finance I},
Publisher = {in preparation},
Year = {2008},
Month = {June},
Key = {fds28898}
}
@book{fds70670,
Author = {A.O. Petters},
Title = {Algebra, Geometry, and Trigonometry: Student and Teacher
Editions},
Publisher = {BRC, Benque-Belize},
Year = {2007},
Month = {August},
Key = {fds70670}
}
@book{fds70667,
Author = {A.O. Petters},
Title = {Scientific Reasoning: Student and Teacher
Editions},
Publisher = {BRC, Benque-Belize},
Year = {2007},
Month = {July},
Key = {fds70667}
}
@book{fds70668,
Author = {A.O. Petters},
Title = {PSE Mathematics: Student and Teacher Editions},
Publisher = {BRC, Benque-Belize},
Year = {2007},
Key = {fds70668}
}
@book{fds9010,
Author = {A. O. Petters and H. Levine and J. Wambsganss},
Title = {Singularity Theory and Gravitational Lensing},
Series = {Progress in Mathematical Physics, Volume
21},
Publisher = {Birkhauser},
Year = {2001},
Month = {June},
url = {http://www.amazon.com/exec/obidos/ASIN/0817636684/qid=1028663985/sr=1-1/ref=sr_1_1/002-1045375-379126},
Key = {fds9010}
}
%% Papers Published
@article{fds157741,
Author = {A. M. Aazami and A.O. Petters},
Title = {A Universal Magnification Theorem for Higher-Order Caustic
Singularities},
Journal = {J. Math. Phys.},
Volume = {50},
Pages = {032501},
Year = {2009},
Month = {November},
url = {http://arxiv.org/abs/0811.3447},
Key = {fds157741}
}
@article{fds139787,
Author = {M. C. Werner and A.O. Petters},
Title = {Magnification Relations for Kerr Lensing and Testing Cosmic
Censorship},
Journal = {Physical Review D},
Volume = {76},
Pages = {064024},
Year = {2007},
Month = {September},
url = {http://xxx.lanl.gov/abs/0706.0132},
Key = {fds139787}
}
@article{fds139786,
Author = {S. Iyer and A.O. Petters},
Title = {Light's Bending Angle due to Black Holes: From the Photon
Sphere to Infinity},
Journal = {General Relativity and Gravitation},
Volume = {39},
Pages = {1563},
Year = {2007},
url = {http://xxx.lanl.gov/abs/gr-qc/0611086},
Key = {fds139786}
}
@article{fds157981,
Author = {C. Keeton and A.O. Petters},
Title = {Testing Theories of Gravity with Black Hole
Lensing},
Booktitle = {Proceedings of the Ninth Marcel Grossmann Meeting on General
Relativity, ed. R. Ruffini},
Year = {2006},
Month = {Summer},
Key = {fds157981}
}
@article{fds47734,
Author = {C. Keeton and A.O. Petters},
Title = {Formalism for Testing Theories of Gravity Using Lensing by
Compact Objects. III. Braneworld Gravity},
Journal = {Phys. Rev. D},
Volume = {73},
Pages = {104032},
Year = {2006},
Month = {May},
url = {http://xxx.lanl.gov/abs/gr-qc/0603061},
Key = {fds47734}
}
@article{fds47733,
Author = {C. Keeton and A.O. Petters},
Title = {Formalism for Testing Theories of Gravity Using Lensing by
Compact Objects. II. Probing Post-Post-Newtonian
Metrics},
Journal = {Phys. Rev. D},
Volume = {73},
Pages = {044024},
Year = {2006},
Month = {March},
url = {http://xxx.lanl.gov/abs/gr-qc/0601053},
Key = {fds47733}
}
@article{fds43287,
Author = {C. Keeton and A.O. Petters},
Title = {Formalism for Testing Theories of Gravity Using Lensing by
Compact Objects. I. Static, Spherically Symmetric
Case},
Journal = {Physical Review D},
Volume = {72},
Pages = {104006},
Year = {2005},
Month = {December},
url = {http://xxx.lanl.gov/abs/gr-qc/0511019},
Key = {fds43287}
}
@article{fds43286,
Author = {C. Keeton and S. Gaudi and A.O. Petters},
Title = {Identifying Lensing by Substructure II. Fold
Lenses},
Journal = {Astrophysical Journal},
Volume = {635},
Pages = {35},
Year = {2005},
Month = {November},
url = {http://xxx.lanl.gov/abs/astro-ph/0503452},
Key = {fds43286}
}
@article{fds15384,
Author = {C. Keeton and S. Gaudi and A.O. Petters},
Title = {Identifying Lensing by Substructure I. Cusp
Lenses},
Journal = {Astrophys. J.},
Volume = {598},
Pages = {138},
Year = {2003},
url = {http://xxx.lanl.gov/abs/astro-ph/0210318},
Key = {fds15384}
}
@article{fds10361,
Author = {A. O. Petters},
Title = {On Relativistic Corrections to Microlensing Effects:
Applications to the Galactic Black Hole},
Journal = {Monthly Notices of the Royal Astronomical
Society},
Volume = {338},
Pages = {457},
Year = {2003},
url = {http://xxx.lanl.gov/ps/astro-ph/0208500},
Key = {fds10361}
}
@article{fds10360,
Author = {S. Frittelli and A. O. Petters},
Title = {Wavefronts, Caustic Sheets, and Caustic Surfing in
Gravitational Lensing},
Journal = {J. Math. Phys.},
Volume = {43},
Pages = {5578},
Year = {2002},
url = {http://xxx.lanl.gov/abs/astro-ph/0208135},
Key = {fds10360}
}
@article{fds10362,
Author = {S. Gaudi and A. O. Petters},
Title = {Gravitational Microlensing Near Caustics II:
Cusps},
Journal = {The Astrophysical Journal},
Volume = {580},
Number = {468},
Year = {2002},
url = {http://xxx.lanl.gov/abs/astro-ph/0206162},
Key = {fds10362}
}
@article{fds10280,
Author = {S. Gaudi and A. O. Petters},
Title = {Gravitational Microlensing Near Caustics I:
Folds},
Journal = {The Astrophysical Journal, 574, 970 (2002)},
Volume = {574},
Number = {970},
Year = {2002},
url = {http://xxx.lanl.gov/abs/astro-ph/0112531},
Key = {fds10280}
}
@article{fds9789,
Author = {A. O. Petters},
Title = {Stable Lens Systems, Lensed Image Magnification,and
Magnification Cross Sections},
Journal = {Proceedings of the Ninth Marcel Grossmann Meeting on General
Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R.
Ruffini},
Publisher = {World Scientific},
Address = {Singapore},
Year = {2001},
Key = {fds9789}
}
@article{fds9790,
Author = {S. Frittelli and A. O. Petters},
Title = {Wavefront Singularities due to an Elliptical
Potential},
Journal = {Proceedings of the Ninth Marcel Grossmann Meeting on General
Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R.
Ruffini},
Publisher = {World Scientific},
Address = {Singapore},
Year = {2001},
Key = {fds9790}
}
@article{fds9791,
Author = {B. S. Gaudi and A. O. Petters},
Title = {Center of Light Curves for Whitney Fold and
Cusp},
Journal = {Proceedings of the Ninth Marcel Grossmann Meeting on General
Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini
(World Scientific,Singapore)},
Year = {2001},
Key = {fds9791}
}
@article{fds9009,
Author = {A. O. Petters and F. Wicklin},
Title = {Fixed Points Due to Gravitational Lenses},
Journal = {J. Math. Phys., 39, 1011},
Year = {1998},
Key = {fds9009}
}
@article{fds9006,
Author = {A. O. Petters and F.J. Wicklin},
Title = {Counting Formulas and Bounds on Number of Fixed Points Due
to Point-Mass Lenses},
Journal = {Proceedings of the Eighth Marcel Grossmann Meeting on
General Relativity 1997, ed. R. Ruffini (World Scientific,
Singapore)},
Year = {1997},
Month = {Summer},
Key = {fds9006}
}
@article{fds9007,
Author = {S. Mao and A. O. Petters and H. Witt},
Title = {Properties of Point Mass Lenses on a Regular Polygon and the
Problem of Maximum Number of Lensed Images},
Journal = {in Proceedings of the Eighth Marcel Grossman Meeting on
General Relativity, ed. R. Ruffini (World Scientific,
Singapore)},
Year = {1997},
Month = {Summer},
Key = {fds9007}
}
@article{fds9008,
Author = {A. O. Petters},
Title = {Some Global Results on Gravitational Lensing},
Journal = {Proceedings of the Eight Marcel Grossman Meeting on General
Relativity, ed. R. Ruffini (World Scientific,
Singapore)},
Year = {1997},
Month = {Summer},
Key = {fds9008}
}
@article{fds9004,
Author = {A. O. Petters},
Title = {Curvature of Caustics and Singularities of Gravitational
Lenses},
Journal = {Proceedings of the Second World Congress of Nonlinear
Analysts ed. V. Lakshmikantham (Elsevier Science Ltd.,
Oxford)},
Year = {1997},
Key = {fds9004}
}
@article{fds9005,
Author = {A. O. Petters},
Title = {Multiplane Gravitational Lensing III. Upper Bound on Number
of Images},
Journal = {J. Math. Phys.},
Volume = {38},
Pages = {1605},
Year = {1997},
Key = {fds9005}
}
@article{fds8999,
Author = {A. O. Petters},
Title = {Lower Bounds on Image Magnification in Gravitational
Lensing},
Journal = {Proc. R. Soc. Lond. A},
Volume = {452},
Pages = {1475},
Year = {1996},
Key = {fds8999}
}
@article{fds9000,
Author = {A. O. Petters},
Title = {A Cusp-Counting Formula for Caustics Due to Multiplane
Gravitational Lensing},
Journal = {Astrophysical Applications of Gravitational Lensing, eds.
C.S. Kochanek and J.N. Hewitt (Klumer Academic,
Dordrecht)},
Year = {1996},
Key = {fds9000}
}
@article{fds9001,
Author = {A. O. Petters},
Title = {Mathematical Aspects of Gravitational Lensing},
Journal = {Proceedings of the Seventh Marcel Grossman Meeting on
General Relativity, Vol. B, eds. R.T. Jantzen and G.M.
Keiser (World Scientific, Singapore)},
Year = {1996},
Key = {fds9001}
}
@article{fds9002,
Author = {A. O. Petters and F.J. Wicklin},
Title = {New Caustic Phenomena for Caustics in Double-Plane
Lensing},
Journal = {Astrophysical Applications of Gravitational Lensing, eds.
C.S. Kochanek and J.N. Hewitt (Klumer Academic,
Dordrecht)},
Year = {1996},
Key = {fds9002}
}
@article{fds9003,
Author = {A. O. Petters and H. Witt},
Title = {Bounds on Number of Cusps Due to Point Mass Gravitional
Lenses with Continuous Matter and Shear},
Journal = {J. Math. Phys.},
Volume = {37},
Number = {2920},
Year = {1996},
Key = {fds9003}
}
@article{fds8998,
Author = {A. O. Petters and F.J. Wicklin},
Title = {Caustics of the Double-Plane Two Point-Mass Gravitational
Lens with Continuous Matter and Shear},
Journal = {Mon. Not. R. Astron. Soc.},
Volume = {277},
Pages = {1399},
Year = {1995},
Month = {Summer},
Key = {fds8998}
}
@article{fds8997,
Author = {A. O. Petters},
Title = {Multiplane Gravitational Lensing II: Global Geometry of
Caustics},
Journal = {J. Math. Phys.},
Volume = {36},
Pages = {4276},
Year = {1995},
Month = {April},
Key = {fds8997}
}
@article{fds8996,
Author = {A. O. Petters},
Title = {Multiplane Gravitational Lensing I: Morse Theory and Image
Counting},
Journal = {J. Math. Phys.},
Volume = {36},
Pages = {4263},
Year = {1995},
Month = {March},
Key = {fds8996}
}
@article{fds8995,
Author = {H. Levine and A. O. Petters},
Title = {Singularities and Gravitational Lensing},
Journal = {Passion des Formes: Hommage a Rene Thom,Vol. 1 (M. Porte,
ed.) E.N.S. Edition, Fontenany-St Cloud},
Year = {1994},
Key = {fds8995}
}
@article{fds9369,
Author = {H. Levine and A. O. Petters and J. Wambsganss},
Title = {Applications of Singularity Theory to Gravitational
Lensing},
Journal = {J. Math. Phys.},
Volume = {34},
Pages = {4781},
Year = {1993},
Key = {fds9369}
}
@article{fds9370,
Author = {H. Witt and A. O. Petters},
Title = {Singularities of the One and Two Point Mass Gravitational
Lens},
Journal = {J. Math. Phys., 34, 4781},
Year = {1993},
Key = {fds9370}
}
@article{fds9371,
Author = {H. Levine and A. O. Petters},
Title = {New Caustic Singularities in Multiple Lens Plane
Gravitational Lensing},
Journal = {Astron. Astrophys.},
Volume = {272},
Number = {L17},
Year = {1993},
Key = {fds9371}
}
@article{fds9372,
Author = {A. O. Petters},
Title = {Arnold's Singularity Theory and Gravitational
Lensing},
Journal = {J. Math. Phys.},
Volume = {34},
Pages = {3555},
Year = {1993},
Key = {fds9372}
}
@article{fds9373,
Author = {A. O. Petters},
Title = {Morse Theory and Gravitational Microlensing},
Journal = {J. Math. Phys.},
Volume = {33},
Pages = {1915},
Year = {1992},
Key = {fds9373}
}
@article{fds9374,
Author = {A. O. Petters and D. Spergel},
Title = {An Analytical Approach to Quasar Variability due to
Microlensing},
Journal = {Gravitational Lenses, eds. R. Kayser, T. Schramm, and L.
Nieser (Lecture Notes in Physics, 406, Springer,
Ber1in)},
Year = {1992},
Key = {fds9374}
}
@article{fds9375,
Author = {A. O. Petters},
Title = {Morse Theory and Gravitational Microlensing},
Journal = {Gravitational Lenses, eds. R. Kayser, T. Schramm, and L.
Nieser (Lecture Notes in Physics 406, Springer,
Ber1in)},
Year = {1992},
Key = {fds9375}
}
%% Papers Submitted
@article{fds157980,
Author = {A. B. Aazami and A.O. Petters},
Title = {A Universal Magnification Theorem II. Generic Caustics up to
Codimension Five},
Year = {2009},
Key = {fds157980}
}
@article{fds148864,
Author = {A.O. Petters and B. Rider and A. M. Teguia},
Title = {A Mathematical Theory of Stochastic Microlensing II. Random
Images, Shear, and the Kac-Rice Formula},
Year = {2008},
Key = {fds148864}
}
@article{fds148865,
Author = {A.O. Petters and B. Rider and A. M. Teguia},
Title = {A Mathematical Theory of Stochastic Microlensing I. Random
Time Delay Functions and Lensing Maps},
Year = {2008},
Key = {fds148865}
}
%% Other
@article{fds47735,
Author = {A.O. Petters},
Title = {Singularities in Gravitational Microlensing, Ph.D.
Thesis},
Journal = {MIT, Department of Mathematics},
Year = {1991},
Key = {fds47735}
}