Peter Olver's Additional Publications

Last updated:   November 18, 2009

Recent (and not so recent) Preprints

  1. Olver, P.J., Moving frames and differential invariants in centro-affine geometry, preprint, University of Minnesota, 2008.
  2. Itskov, V., Olver, P.J., and Valiquette, F., Lie completion of pseudo-groups, preprint, University of Minnesota, 2009.
  3. Mari-Beffa, G., and Olver, P.J., Poisson structures for geometric curve flows on semi-simple homogeneous spaces, preprint, University of Minnesota, 2009.
  4. Olver, P.J., Dispersive quantization, Amer. Math. Monthly, to appear.
  5. Olver, P.J., Lectures on moving frames, preprint, University of Minnesota, 2008.
  6. Olver, P.J., Invariant variational problems and invariant flows via moving frames, preprint, University of Minnesota, 2007.
  7. Olver, P.J., Invariant theory of biforms, preprint, 1986.
  8. Olver, P.J., Differential hyperforms I, preprint, 1982.

Appendices and Chapters in Books

  1. Olver, P.J., Lie algebras and Lie groups, in: Encyclopedia of Nonlinear Science, A. Scott, ed., Routledge, New York, 2004.
  2. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.
  3. Olver, P.J., and Vorob'ev, E.M., Nonclassical and conditional symmetries, in: CRC Handbook of Lie Group Analysis of Differential Equations, vol. 3, N.H. Ibragimov, ed., CRC Press, Boca Raton, Fl., 1996, pp. 291-328.
  4. Olver, P.J., Sapiro, G., and Tannenbaum, A., Differential invariant signatures and flows in computer vision: a symmetry group approach, in: Geometry-Driven Diffusion in Computer Vision, B. M. Ter Haar Romeny, ed., Kluwer Acad. Publ., Dordrecht, the Netherlands, 1994, pp. 255-306.
  5. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in higher dimensions, appendix in: Quasi-Exact Solvability; A.G. Ushveridze, Adam Hilger, Bristol, 1994.
  6. Olver, P.J., How to find the symmetry group of a differential equation, appendix in: Group Theoretic Methods in Bifurcation Theory, D.H. Sattinger, Lecture Notes in Mathematics, vol. 762, Springer-Verlag, New York, 1979.

Contributions to Conference Proceedings

  1. Olver, P.J., and Pohjanpelto, J., Pseudo-groups, moving frames, and differential invariants, in: Symmetries and Overdetermined Systems of Partial Differential Equations, M. Eastwood and W. Miller, Jr., eds., IMA Volumes in Mathematics and Its Applications, vol. 144, Springer-Verlag, New York, 2008, pp. 127-149.
  2. Olver, P.J., and Pohjanpelto, J., Differential invariants for Lie pseudo-groups, in: Gröbner Bases in Symbolic Analysis; M. Rosenkranz, D. Wang, eds, Radon Series Comp. Appl. Math., vol. 2, Walter de Gruyter, Berlin, 2007, pp. 217-243.
  3. Olver, P.J., and Pohjanpelto, J., Moving frames and differential invariants for Lie pseudo-groups, in: Symmetry and Perturbation Theory, G. Gaeta, R. Vitolo and S. Walcher, eds., World Scientific, Singapore, 2007, pp. 172-180.
  4. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.
  5. Rathi, Y., Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant surface evolutions for 3D image segmentation, in: Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, E.R. Dougherty, J.T. Astola, K.O. Egiazarian, N.M. Nasrabadi, and S.A. Rizvi, eds., vol. 6064, SPIE Press, Bellingham, Wash., 2006, pp. 606401.
  6. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  7. Olver, P.J., and Pohjanpelto, J., Regularity of pseudogroup orbits, in: Symmetry and Perturbation Theory, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, S. Terracini, eds., World Scientific, Singapore, 2005, pp. 244-254.
  8. Olver, P.J., An introduction to moving frames, in: Geometry, Integrability and Quantization; vol. 5, I.M. Mladenov and A.C. Hirschfeld, eds., Softex, Sofia, Bulgaria, 2004, pp. 67-80.
  9. Olver, P.J., Nonlocal symmetries and ghosts, in: New Trends in Integrability and Partial Solvability, A.B. Shabat et. al., eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2004, pp. 199-215.
  10. Georgiou, T., Olver, P.J., and Tannenbaum, A., Maximal entropy for reconstruction of back projection images, in: Mathematical Methods in Computer Vision, P.J. Olver and A. Tannenbaum, eds., IMA Volumes in Mathematics and its Applications, vol. 133, Springer-Verlag, New York, 2003, pp. 57-64.
  11. Olver, P.J., Moving frames: a brief survey, in: Symmetry and Perturbation Theory, D. Bambusi, M. Cadoni and G. Gaeta, eds., World Scientific, Singapore, 2001, pp. 143-150.
  12. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.
  13. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.
  14. Fels, M., and Olver, P.J., Moving frames and moving coframes, in: Algebraic Methods in Physics, Y. Saint-Aubin and L. Vinet, eds., CRM Series in Math. Phys., Springer-Verlag, New York, 2001, pp. 47-64.
  15. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.
  16. Olver, P.J., Moving frames, RIMS Kokyuroku 1150 (2000) 114-124.
  17. Li, Y.A., Olver, P.J., and Rosenau, P., Non-analytic solutions of nonlinear wave equations, in: Nonlinear Theory of Generalized Functions, M. Grosser, G. Hormann, M. Kunzinger, and M. Oberguggenberger, eds., Research Notes in Mathematics, vol. 401, Chapman and Hall/CRC, New York, 1999, pp. 129-145.
  18. Olver, P.J., A quasi-exactly solvable travel guide, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 1, H.-D. Doebner, W. Scherer, P. Nattermann, eds., World Scientific, Singapore, 1997, pp. 285-295.
  19. Heredero, R.H., Olver, P.J., Classification of invariant wave equations, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 2, H.-D. Doebner, W. Scherer, C. Schulte, eds., World Scientific, Singapore, 1997, pp. 1010-1016.
  20. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.
  21. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant gradient flows, in: ICAOS '96: Images, Wavelets and PDE's, M.-O. Berger, et. al., eds., Lecture Notes in Control and Information Sciences, vol. 219, Springer-Verlag, New York, 1996, pp. 194-200.
  22. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edge maps, anisotropic diffusion, and active contours, Acta Appl. Math. 59 (1999) 45-77.
  23. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A., A gradient surface evolution approach to 3D segmentation, in: Proceedings of IS&T, Minneapolis, MN, 1995
  24. Finkel, F., Gonzalez-Lopez, A., Kamran, N., Olver, P.J., and Rodriguez, M.A., Lie algebras of differential operators and partial integrability, in: Proceedings of IV Workshop on Differential Geometry and its Applications; Santiago de Compostela, Spain, 1995.
  25. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Gradient flows and geometric active contour models, in: Fifth International Conference on Computer Vision, IEEE Computer Soc. Press, Cambridge, Mass., 1995, pp. 810-815.
  26. Olver, P.J., Higher order models for water waves, in: Geometrical Methods in Fluid Dynamics, R. Salmon, B. Ewing-Deremer, eds., Woods Hole Oceanographic Institution, Technical Report WHOI-94-12, Woods Hole, MA, 1994, pp. 327-331.
  27. Anderson, I.M., Kamran, N., and Olver, P.J., Internal symmetries of differential equations, in: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N.H. Ibragimov, M. Torrisi, and A. Valenti, eds., Kluwer, Dordrecht, The Netherlands, 1993, pp. 7-21.
  28. Olver, P.J., Canonical forms for biHamiltonian systems, in: The Verdier Memorial Conference on Integrable Systems, O. Babelon, P. Cartier and Y. Kosmann-Schwarzbach eds., Progress in Math., Birkhäuser, Boston, 1993, pp. 239-249.
  29. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, in: Group Theoretic Methods in Physics, M.A. del Olmo, M. Santander, and J. Mateos Guilarte, eds., Proc. XIX International Colloquium, Anales de Física Monografias, Editorial Ciemat, Madrid, 1992, Vol. I, pp. 233-236.
  30. Olver, P.J., Canonical forms for compatible biHamiltonian systems, in: Solitons and Chaos, I. Antoniou and F. Lambert, eds., Springer-Verlag, New York, 1991, pp. 171-179.
  31. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Lie algebras of first order differential operators in two complex variables, in: Differential Geometry, Global Analysis, and Topology, A. Nicas and W.F. Shadwick, eds., Canadian Math. Soc. Conference Proceedings, vol. 12, Amer. Math. Soc., Providence, R.I., 1991, pp. 51-84.
  32. Olver, P.J., Canonical anisotropic elastic moduli, in: Modern Theory of Anisotropic Elasticity and Applications, J.J. Wu, T.C.T. Ting and D.M. Barnett, eds., SIAM, Philadelphia, 1991, pp. 325-339.
  33. Olver, P.J., Internal symmetries of differential equations, in: Differential Equations and Computer Algebra, M. Singer, ed., Academic Press, New York, 1991, pp. 1-28.
  34. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.
  35. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.
  36. Olver, P.J., Generalized symmetries, in: XV International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed., World Scientific, Singapore, 1987, pp. 216-228.
  37. Olver, P.J., Conservation laws in continuum mechanics, in: Non-classical Continuum Mechanics, R.J. Knops and A.A. Lacey, eds., London Math. Soc. Lecture Note Series #122, Cambridge Univ. Press, Cambridge, 1987, pp. 96-107.
  38. Olver, P.J., BiHamiltonian systems, in: Ordinary and Partial Differential Equations, B.D. Sleeman and R.J. Jarvis, eds., Pitman Research Notes in Mathematics Series, No. 157, Longman Scientific and Technical, New York, 1987, pp. 176-193.
  39. Olver, P.J., Invariant theory and differential equations, in: Invariant Theory, S.S. Koh, ed., Lecture Notes in Mathematics, vol. 1278, Springer-Verlag, New York, 1987, pp. 62-80.
  40. Olver, P.J., Noether's theorems and systems of Cauchy-Kovalevskaya type, in: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, B. Nicholaenko, D.D. Holm and J.M. Hyman, eds., Lectures in Applied Math., vol. 23, part 2, Amer. Math. Soc., Providence, R.I., 1986, pp. 81-104.
  41. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.
  42. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.
  43. Olver, P.J., and Shakiban, C., A resolution of the Euler operator, in: Proceedings of the Eighth National Mathematics Conference, M. Nouri-Moghadam, ed., Arya-Mehr Univ. Tech., Tehran, Iran, 1977, pp. 325-337.

Book Reviews

  1. Gilmore, R., Lie Groups, Physics, and Geometry. An Introduction for Physicists, Engineers, and Chemists, Cambridge University Press, New York, 2008 — in: Physics Today 62 (3) (2009) 55-56.
  2. Schwarz, F., Algorithmic Lie Theory for Solving Ordinary Differential Equations, Chapman & Hall/CRC, Boca Raton, Fl, 2008 — in: Math. Reviews, MR2351266 (2009a:34015).
  3. Bryant, R., Griffiths, P., and Grossman, D., Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, University of Chicago Press, 2003 — in: Bull. Amer. Math. Soc. 42 (2005) 407-412.
  4. Lee, J.M., Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218, Springer-Verlag, New York, 2003 — in: SIAM Review 46 (2004) 179-180.
  5. Hydon, P.E., Symmetry Methods for Differential Equations, Cambridge University Press, Cambridge, 2000 — in: Zeit. Angew. Math. Mechanik 81 (2001) 612.
  6. Andreev, V.K., Kaptsov, O.V., Pukhanachov, V.V., and Rodinov, A.A., Applications of Group-Theoretical Methods in Hydrodynamics, Kluwer Academic Publ., Dordrecht, the Netherlands, 1998 — in: Zeit. Angew. Math. Physik 52 (2001) 896-897.
  7. Duistermaat, J.J., and Kolk, J.A.C., Lie Groups, Springer-Verlag, New York, 1999 — in: SIAM Review 43 (2001) 399-400.
  8. Krasil'shchik, I.S., and Vinogradov, A.M. (eds.), Symmetries of Differential Equations in Mathematical Physics, American Mathematical Society, 1998 — in: Bull. Amer. Math. Soc. 37 (2000) 369-371.
  9. Fushchich, W.I., and Nikitin, A.G., Symmetries of Equations of Quantum Mechanics, Allerton Press, New York, 1994 — in: Foundations of Physics 77 (1995), 297.
  10. Dorfman, I., Dirac Structures and Integrability of Nonlinear Evolution Equations, Nonlinear Science: Theory and Applications, J. Wiley & Sons, New York, 1993 — in: Bull. Amer. Math. Soc. 31 (1994), 305-308.
  11. Zharinov, V.V., Geometrical Aspects of Partial Differential Equations, World Scientific, Singapore, 1992 — in: SIAM Review 35 (1993), 675-676.
  12. Golubitsky, M., and Stewart, I., Fearful Symmetry: Is God a Geometer?, Blackwell, Oxford, 1992 — in: SIAM News 26(1) (1993), 9, 19.
  13. Stephani, H., Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989 — in: SIAM Review 33 (1991), 330-332.
  14. Rogers, C., and Ames, W.F., Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, New York, 1989 — in: Math. of Computation, 55 (1990), 873-874.
  15. Bluman, G.W., and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989 — in: SIAM Review 32 (1990), 517-519.
  16. Fushchich, W.I., and Nikitin, A.G., Symmetries of Maxwell's Equations, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1987 — in: American Scientist 77 (1989), 297.
  17. Fushchich, W.I., and Nikitin, A.G., Symmetries of Maxwell's Equations, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1987 — in: Bull. Amer. Math. Soc. 19 (1988), 545-550.
  18. Ibragimov, N.H., Transformation Groups Applied to Mathematical Physics, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1985 — in: American Scientist 75 (1987), 211-212.