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}
}