Research Group in Global Analysis and Applications

http://globanal.upol.cz

Prof. RNDr. Olga Krupková, DrSc. photo

Positions:Head of Department of Mathematics, Faculty of Science, The University of Ostrava
Adjunct Professor, Faculty of Science, Technology and Engineering, La Trobe University, Melbourne (honorary position)
Professor, Faculty of Science, Palacký University, Olomouc (part time)
Addresses:Department of Mathematics
Faculty of Science, The University of Ostrava
30. dubna 22, 701 03 Ostrava, Czech Republic
&
Department of Mathematics and Statistics
Faculty of Science, Technology and Engineering
School of Engineering and Mathematical Sciences
La Trobe University, Bundoora, 3086 Victoria, Australia
Phone:+420 597 092 100
Fax:+420 596 120 478
E-mail:name@osu.cz, name@latrobe.edu.au
Homepage:http://globanal.upol.cz/krupkova.html
http://www.latrobe.edu.au/mathstats/staff/krupkova/index.html

List of Publications


Books

  1. D. Krupka and O. Krupková, Topology and Geometry (in Czech), (SPN, Praha, 1989) 404 pp., ISBN 80-000-0000-0.
  2. O. Krupková, The Geometry of Ordinary Variational Equations, Lecture Notes in Mathematics 1678 (Springer, Berlin, 1997) 251 pp., ISBN 3-540-63832-6.
  3. K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), Global Analysis and Applied Mathematics, AIP Conf. Proc. 729 (American Institute of Physics, New York, 2004) 398 pp., ISBN 0-7354-0209-4.
  4. O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007 (World Scientific, Singapore, 2008) 717 pp., ISBN-13 978-981-279-060-6, 10 981-279-060-8.
  5. O. Krupková and D.J. Saunders (Eds.), Variations, Geometry and Physics, Volume in honour of D. Krupka's 65th birthday (Nova Science Publishers, New York, 2009) 360 pp., ISBN 978-1-60456-920-9.

Book Chapters

  1. O. Krupková, A new look at Dirac's theory of constrained systems, In: Gravity, Particles and Space-Time, Volume in Honour of D. Ivanenko (World Scientific, Singapore, 1996), 507-518, ISBN 981-02-2668-3.
  2. O. Krupková, Differential systems in higher-order mechanics. In: Proceedings of the Seminar on Differential Geometry, Mathematical Publications 2 (Silesian University, Opava 2000) 87-130, ISBN 80-7248-104-5.
  3. O. Krupková, Helmholtz conditions in the geometry of second order ordinary differential equations, In: Differential Geometric Methods in Mechanics and Field Theory, Volume in Honour of W. Sarlet (Academia Press, Gent, 2007) 91-114, ISBN 978-90-382-1128-2.
  4. O. Krupková and G.E. Prince, Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations, In: Handbook of Global Analysis (Elsevier, 2008) 837-904, ISBN 978-0-444-52833-9.
  5. O. Krupková, Lepage Forms in the Calculus of Variations, In: Variations, Geometry and Physics, Volume in honour of D. Krupka's 65th birthday (Nova Science Publishers, New York, 2009) 29-56, ISBN 978-1-60456-920-9.
  6. O. Krupková, Variational Equations on Manifolds, In: Advances in Mathematics Research, Vol. 9 (Nova Science Publishers, New York, 2009) 201-274, ISBN: 978-1-60692-179-1.

Papers

  1. M. Štefanová and O. Štěpánková, Invariance of motion equations and variationality conditions (in Czech), Charles University, Prague, March 1982; paper won a prize at the Czechoslovak Students' Scientific Conference, Prague, 1982.
  2. O. Štěpánková, Generalized regularity in Hamiltonian mechanics (in Czech), Charles University, Prague, March 1984, 29 pp.; paper won a prize at the Czechoslovak Students' Scientific Conference, Prague, 1984.
  3. D. Krupka and O. Štěpánková, On the Hamilton form in second order calculus of variations, In: Geometry and Physics, Proc. Internat. Meeting, Florence, 1982, M. Modugno, Ed. (Pitagora, Bologna, 1983) 85-102, ISBN 88-371-0280-1.
  4. O. Štěpánková, The local inverse problem of the calculus of variations in higher order Hamiltonian mechanics, In: Geometrical Methods in Physics, Proc. Conf. on Diff. Geom. And Appl., Nové Město na Moravě, September 1983, Part 2, D. Krupka, Ed. (J.E. Purkyně University, Brno, Czechoslovakia, 1984) 275-287.
  5. M. Štefanová and O. Štěpánková, Variationality and invariance of systems of partial differential equations, Scripta Fac. Sci. Nat. UJEP Brunensis (Physica) 5 (1985) 283-288.
  6. O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, I. Regularity, Arch. Math. (Brno) 22 (1986) 97-120.
  7. O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, II. Inverse problem, Arch. Math. (Brno) 23 (1987) 155-170.
  8. O. Krupková, A note on the Helmholtz conditions, In: Differential Geometry and Its Applications, Proc. Conf., Brno, August 1986, Communications, D. Krupka and A. Švec, Eds. (J.E. Purkyně University, Brno, Czechoslovakia, 1987) 181-188.
  9. O. Krupková, Liouville and Jacobi theorems for vector distributions, In: Differential Geometry and Its Applications, Proc. Conf., Opava, August 1992, O. Kowalski and D. Krupka, Eds. (Math. Publications 1, Silesian University, Opava, Czechoslovakia, 1993) 75-88, ISBN 80-901581-0-2.
  10. O. Krupková and A. Vondra, On some integration methods for connections on fibered manifolds, In: Differential Geometry and Its Applications, Proc. Conf., Opava, August 1992, O. Kowalski and D. Krupka, Eds. (Math. Publications 1, Silesian University, Opava, Czechoslovakia, 1993) 89-102, ISBN 80-901581-0-2.
  11. O. Krupková, On the inverse problem of the calculus of variations for ordinary differential equations, Math. Bohemica 118 (1993) 261-276.
  12. O. Krupková, Variational metrics on R TM and the geometry of nonconservative mechanics, Math. Slovaca 44 (1994) 315-335.
  13. O. Krupková, A geometric setting for higher-order Dirac-Bergmann theory of constraints, J. Math. Phys. 35 (1994) 6557-6576.
  14. O. Krupková, Higher-order constrained systems on fibered manifolds: An exterior differential systems approach, In: New Developments in Differential Geometry, Proc. Colloq. on Diff. Geom., Debrecen, 1994, L. Tamássy and J. Szenthe, Eds. (Kluwer, Dordrecht, 1996) 255-278, ISBN 0-7923-3822-7.
  15. O. Krupková, Symmetries and first integrals of time-dependent higher-order constrained systems, J. Geom. Phys. 18 (1996) 38-58.
  16. O. Krupková, Noether theorem and first integrals of constrained Lagrangean systems, Math. Bohemica 122 (1997) 257-265.
  17. O. Krupková, Mechanical systems with non-holonomic constraints, J. Math. Phys. 38 (1997) 5098-5126.
  18. J. Musilová, O. Krupková and D. Krupka, The variational sequence in Physics (in Czech), Čs. čas. fyz. A 48 (1998), Issue in honour of M. Černohorský, 329-341.
  19. O. Krupková, On the geometry of non-holonomic mechanical systems, In: Differential Geometry and Applications, Proc. Conf., Brno, August 1998, I. Kolář, O. Kowalski, D. Krupka and J. Slovák, Eds. (Masaryk University, Brno, 1999) 533-546, ISBN 80-210-2097-0, Electronic edition: EMIS.
  20. O. Krupková, Higher-order mechanical systems with constraints, J. Math. Phys. 41 (2000) 5304-5324.
  21. O. Krupková and J. Musilová, The relativistic particle as a mechanical system with non-holonomic constraints, J. Phys. A: Math. Gen. 34 (2001) 3859-3876.
  22. O. Krupková, Hamiltonian field theory revisited: A geometric approach to regularity, In: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, Eds. (Debrecen University, Debrecen, 2001) 187-207.
  23. O. Krupková and D. Smetanová, On regularization of variational problems in first order field theory, Rend. Circ. Mat. Palermo, Serie II, Suppl. 66 (2001) 133-140.
  24. O. Krupková and D. Smetanová, Legendre transformation for regularizable Lagrangians in field theory, Letters in Math. Phys. 58 (2001) 189-204.
  25. O. Krupková, Hamiltonian field theory, J. Geom. Phys. 43 (2002) 93-132.
  26. O. Krupková, Recent results in the geometry of constrained systems, Reports on Math. Phys. 49 (2002) 269-278.
  27. P. Volný and O. Krupková, Hamilton equations for non-holonomic mechanical systems, In: Differetial Geometry and its Applications, Proc. Conf., Opava 2001 (Mathematical Publications 3, Silesian University, Opava, 2003) 369-380, ISBN 80-7248-166-5.
  28. O. Krupková, Non-variational Hamiltonian structures, Anal. Univ. "Al. I. Cuza" Iasi, Ser. Matematica 49 (2) (2003), Issue in honour of R. Miron, 266-288.
  29. A. Haková and O. Krupková, Variational first-order partial differential equations, J. Differential Equations 191 (2003) 67-89.
  30. O. Krupková, Variational metric structures, Publ. Math. Debrecen 62 (2003), Issue in honour of L. Tamássy, 461-495.
  31. O. Krupková, The geometry of variational equations, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 19-38, ISBN 0-7354-0209-4.
  32. D. Krupka, O. Krupková, G.E. Prince, and W. Sarlet, Contact symmetries and variational sequences, In: Proc. 9th Int. Conf. on Diff. Geom. & Appl., J. Bureš, O. Kowalski, D. Krupka and J. Slovák (Eds.), Prague, August 2004 (Charles University, Prague, 2005) 605-615.
  33. O. Krupková and J. Musilová, Non-holonomic variational systems, Reports on Math. Phys. 55 (2005) 211-220.
  34. O. Krupková and M. Swaczyna, Horizontal and contact forms on constraint manifolds, Rend. Circ. Mat. Palermo, Serie II, Suppl. 75 (2005) 259-267.
  35. O. Krupková and P. Volný, Euler-Lagrange and Hamilton equations for non-holonomic systems in field theory, J. Phys. A: Math. Gen. 38 (2005) 8715-874.
  36. O. Krupková, Partial differential equations with differential constraints, J. Differential Equations 220 (2006) 354-395.
  37. O. Krupková and P. Volný, Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems, Lobachevskii Journal of Mathematics 23 (2006) 95-150.
  38. O. Krupková, The canonical distribution in nonholonomic mechanics and field theory, In: Proc. of the XV International Workshop on Geometry and Physics, Puerto de la Cruz, Tenerife, Canary Islands, Spain, September 2006, D. Iglesias Ponte, J.C. Marrero González, F. Matín Cabrera, E. Padrón Fernández and D. Sosa Martín (Eds.), Publ. de la RSME 11 (Real Sociedad Matemática Espanola, Madrid, 2007) 167-176, ISBN 978-84-935196-1-2.
  39. D. Krupka, O. Krupková, G. Prince and W. Sarlet, Contact symmetries of the Helmholtz form, Differential Geometry and Applications 25 (2007) 518-542.
  40. O. Krupková, Variational exterior differential systems, In: Symmetry and Perturbation Theory, Proc. Int. Conf. SPT, Otranto, June 2007, G. Gaeta, R. Vitolo and S. Walcher (Eds.), (World Scientific, Singapore, 2007) 124-131, ISBN 978-981-277-616-7, 981-277-616-8.
  41. O. Krupková and G.E. Prince, Lepage forms, closed two-forms and second order ordinary differential equations, Russian Mathematics (Izv. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 1-16.
  42. D. Krupka and O. Krupková, Contact symmetries and variational PDE’s, Acta Appl. Math. 101 (1-3) (2008), A special issue dedicated to the 60th anniversary of Valentin Lychagin, 163-176.
  43. O. Krupková, J. Volná and P. Volný, Constrained Lepage forms, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 627-633, ISBN-13 978-981-279-060-6, ISBN-10 981-279-060-8.
  44. O. Krupková, Variational Equations on Manifolds, Expert Commentary, In: Advances in Mathematics Research, Vol. 9 (Nova Science Publishers, New York, 2009) 295-299, ISBN: 978-1-60692-179-1.
  45. O. Krupková and D. Smetanová, Lepage equivalents of second order Euler—Lagrange forms and the inverse problem of the calculus of variations, J. Nonlinear Math. Phys. 16 (2009) 1–16.
  46. O. Krupková and J. Musilová, Nonholonomic forces and the Mach Principle in the Special Relativity Theory, In: Ernst Mach: Physics-Philosophy-Education, Proc. Conf. in honour of Ernst Mach's 170th birthday, Brno, Czech Republic, 2008 (Masaryk University, Brno, 2009), (in Czech), 123-126.
  47. O. Krupková, Noether Theorem, 90 years on, In: Geometry an Physics, Proc. XVII International Fall Workshop on Geometry and Physics, Castro Urdiales, Spain, 2008, AIP Conf. Proceedings (American Institute of Physics, New York, 2009), 159-170.
  48. O. Krupková, The nonholonomic variational principle, J. Phys. A: Math. Theor. 42 (2009) 185201.
  49. D. Krupka, O. Krupková and D.J. Saunders, The Cartan form and its generalizations in the calculus of variations, Int. J. Geom. Met. Mod. Phys. 7 (4) (2010), in press.
  50. O. Krupková and R. Malíková, Helmholtz conditions and their generalizations, Balkan J. Geom. Appl., to be published.

Dissertations

  1. O. Štěpánková, The inverse variational problem in mechanics (in Czech), MSc. Thesis (Charles University, Prague, May 1984) 63 pp.
  2. O. Krupková, Variational Analysis on Fibered Manifolds over One-dimensional Bases, PhD Thesis (Silesian University, Opava & Charles University, Prague, 1992) 67 pp.
  3. O. Krupková, A Geometric Theory of Variational Ordinary Differential Equations, Habilitation Thesis (Silesian University, Opava & Masaryk University, Brno, 1995) 165 pp.
  4. O. Krupková, Geometry of Lepagean 2-forms, DrSc. Thesis (Silesian University, Opava & Masaryk University, Brno) 1997.

Unpublished Preprints

  1. O. Krupková, Hamilton-Jacobi distributions, Preprint (J.E. Purkyně University Brno, 1990) 40 pp.
  2. O. Krupková and J. Musilová, Constraint Helmholtz conditions, Preprint 6/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 10 pp.
  3. O. Krupková and M. Swaczyna, The non-holonomic variational principle, Preprint 8/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 34 pp.
  4. O. Krupková and D.J. Saunders, Affine duality, and Lagrangian and Hamiltonian systems, Preprint Series in Global Analysis and Applications 4/2005 (Dept. of Algebra and Geometry, Palacký University, Olomouc) 11 pp.
  5. O. Krupková and J. Musilová, Non-holonomic relativistic mechanics: A unified approach to particles with non-zero mass and massless particles, Preprint Series in Global Analysis and Applications 7/2006 (Dept. of Algebra and Geometry, Palacký University, Olomouc) 13 pp.