Richard Cushman

Adjunct Professor

Department of Mathematics and Statistics


Contact information

Phone

Office: 403.220.3936

Location

Office : MS564

Publications

Book

  • Beukers, Frits and Cushman, Richard. The complex geometry of the spherical pendulum 292. Amer. Math. Soc., 2002. 47-70. Print.
  • Cushman, Richard and Bates, Larry. Global aspects of classical integrable systems Birkh\"auser Verlag, 1997. xvi+435. Print.
  • Cushman, Richard and Hermans, J.. The rolling disc 19. Birkh\"auser, 1996. 21-60. Print.
  • Kaplan, Samuel R., Cushman, Richard, Hu, Sen, Llibre, Jaume, McCord, Christopher, Saari, Donald G. and Xia, Zhihong. Directions of {H}amiltonian dynamics and celestial mechanics 198. Amer. Math. Soc., 1996. 229-240. Print.
  • Cushman, Richard and Hoveijn, I.. Visualizing special motions of the {E}uler top 4. World Sci. Publ., River Edge, NJ, 1995. 153-167. Print.
  • Bridges, T. J., Cushman, Richard and MacKay, R. S.. Dynamics near an irrational collision of eigenvalues for symplectic mappings 4. Amer. Math. Soc., 1995. 61-79. Print.
  • Cushman, Richard. Geometry of perturbation theory 332. Plenum, 1994. 89-101. Print.
  • Cohen, A. M. and Cushman, Richard. Gr\"obner bases and standard monomial theory 109. Birkh\"auser Boston, 1993. 41-60. Print.
  • Cushman, Richard. A survey of normalization techniques applied to perturbed {K}eplerian systems 1. Springer, 1992. 54-112. Print.
  • Cushman, Richard and Sjamaar, Reyer. On singular reduction of {H}amiltonian spaces 99. Birkh\"auser Boston, 1991. 114-128. Print.
  • Arms, Judith M., Cushman, Richard and Gotay, Mark J.. A universal reduction procedure for {H}amiltonian group actions 22. Springer, 1991. 33-51. Print.
  • Cushman, Richard and Meer, J.. The {H}amiltonian {H}opf bifurcation in the {L}agrange top 1416. Springer, 1990. 26-38. Print.
  • Cushman, Richard and Sanders, J. A.. A survey of invariant theory applied to normal forms of vectorfields with nilpotent linear part 19. Springer, 1990. 82-106. Print.
  • Cushman, Richard and Sanders, Jan A.. Nilpotent normal form in dimension {$4$} 37. Springer, 1987. 61-66. Print.
  • Cushman, Richard and Sanders, Jan A.. Invariant theory and normal form of {H}amiltonian vectorfields with nilpotent linear part 8. Amer. Math. Soc., 1987. 353-371. Print.
  • Cushman, Richard and Sanders, Jan A.. Nilpotent normal forms and representation theory of {${\rm sl}(2,{\bf R})$} 56. Amer. Math. Soc., 1986. 31-51. Print.
  • Cushman, Richard and Kn{\"o}rrer, H.. The energy momentum mapping of the {L}agrange top 1139. Springer, 1985. 12-24. Print.
  • Sanders, J. A. and Cushman, Richard. Abelian integrals and global {H}opf bifurcations 1125. Springer, 1985. 87-98. Print.
  • Cushman, Richard. Normal form for {H}amiltonian vectorfields with periodic flows 6. Reidel, 1984. 125-144. Print.
  • Cushman, Richard. Periodic solutions of the autonomous {J}osephson equation 985. Springer, 1983. 319-326. Print.
  • Cushman, Richard. Morse theory and the method of averaging 70. Dekker, 1981. 25-37. Print.
  • Burgoyne, N. and Cushman, Richard. Normal forms for real linear {H}amiltonian systems Math Sci Press, 1977. 483-529. Lie Groups: History Frontiers and Appl., Vol. VII. Print.
  • Cushman, Richard. The momentum mapping of the harmonic oscillator Academic Press, 1974. 323-342. Print.

Journal article

  • Efstathiou, K., Cushman, Richard and Sadovski{\'{\i}}, D. A.. "Fractional monodromy in the {$1:-2$} resonance". Advances in Mathematics 209.1 (2007): 241-273. Print.
  • Cushman, Richard and Kallen, Wilberd. "A new interpretation for the mass of a classical relativistic particle". Differential Geometry and its Applications 24.3 (2006): 230-234. Print.
  • Cushman, Richard and Duistermaat, J. J.. "Nearly flat falling motions of the rolling disk". Regular \& Chaotic Dynamics. International Scientific Journal 11.1 (2006): 31-60. Print.
  • Cushman, Richard and Kallen, Wilberd. "Adjoint and coadjoint orbits of the {P}oincar\'e group". Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications 90.1-2 (2006): 65-89. Print.
  • Bates, Larry and Cushman, Richard. "Complete integrability beyond {L}iouville-{A}rnol\cprime d". Rep. Math. Phys. 56.1 (2005): 77-91. Print.
  • Bates, Larry, Cushman, Richard and Savev, Emil. "The rotation number and the herpolhode angle in {E}uler's top". Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physiques Appliqu\'ees 56.2 (2005): 183-191. Print.
  • Bates, Larry and Cushman, Richard. "Removing the cocycle in a momentum map". JP Journal of Geometry and Topology 5.2 (2005): 103-107. Print.
  • Dullin, Holger, Giacobbe, Andrea and Cushman, Richard. "Monodromy in the resonant swing spring". Physica D. Nonlinear Phenomena 190.1-2 (2004): 15-37. Print.
  • Efstathiou, K., Cushman, Richard and Sadovski{\'{\i}}, D. A.. "Hamiltonian {H}opf bifurcation of the hydrogen atom in crossed fields". Physica D. Nonlinear Phenomena 194.3-4 (2004): 250-274. Print.
  • Bates, Larry and Cushman, Richard. "The odd symplectic group in geometry". International Journal of Pure and Applied Mathematics 17.1 (2004): 1-8. Print.
  • Giacobbe, A., Cushman, Richard, Sadovski{\'{\i}}, D. A. and Zhilinski{\'{\i}}, B. I.. "Monodromy of the quantum {$1:1:2$} resonant swing spring". Journal of Mathematical Physics 45.12 (2004): 5076-5100. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Erratum: ``{D}ifferential structure of orbit spaces'' [{C}anad. {J}. {M}ath. {\bf 53} (2001), no. 4, 715-755; \refmr {MR}1848504 (2002j:53109)\endrefmr]". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 55.2 (2003): 247. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Erratum: ``{D}ifferential structure of orbit spaces'' [{C}anad. {J}. {M}ath. {\bf 53} (2001), no. 4, 715-755; {MR}1848504 (2002j:53109)]". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 55.2 (2003): 247. Print.
  • Efstathiou, K., Sadovski{\'{\i}}, D. A. and Cushman, Richard. "Linear {H}amiltonian {H}opf bifurcation for point-group-invariant perturbations of the {$1:1:1$} resonance". The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences 459.2040 (2003): 2997-3019. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "A nonholonomic oscillator". Rep. Math. Phys. 50.1 (2002): 85-98. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Nonholonomic reduction for free and proper actions". Regular \& Chaotic Dynamics. International Scientific Journal 7.1 (2002): 61-72. Print.
  • Cushman, Richard and Zhilinskii, Boris. "Monodromy of a two degrees of freedom {L}iouville integrable system with many focus-focus singular points". Journal of Physics. A. Mathematical and General 35.28 (2002): L415-L419. Print.
  • Cushman, Richard. "Sign of the monodromy for {L}iouville integrable systems". Annales Henri Poincar\'e. A Journal of Theoretical and Mathematical Physics 3.5 (2002): 883-894. Print.
  • Cushman, Richard and Roberts, Mark. "Poisson structures transverse to coadjoint orbits". Bulletin des Sciences Math\'ematiques 126.7 (2002): 525-534. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Differential structure of orbit spaces". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 53.4 (2001): 715-755. Print.
  • Cushman, Richard and Duistermaat, J. J.. "Non-{H}amiltonian monodromy". J. Differential Equations 172.1 (2001): 42-58. Print.
  • Cushman, Richard and Sadovski{\'{\i}}, D. A.. "Monodromy in the hydrogen atom in crossed fields". Physica D. Nonlinear Phenomena 142.1-2 (2000): 166-196. Print.
  • Bates, Larry and Cushman, Richard. "What is a completely integrable nonholonomic dynamical system?". Rep. Math. Phys. 44.1-2 (1999): 29-35. Print.
  • Cushman, Richard, Ferrer, Sebasti and Han{\ss}mann, Heinz. "Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator". Nonlinearity 12.2 (1999): 389-410. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Hamiltonian mechanics on principal bundles". Comptes Rendus Math\'ematiques de l'Acad\'emie des Sciences. La Soci\'et\'e Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada 21.2 (1999): 60-64. Print.
  • Cushman, Richard and Sadovski{\'{\i}}, D. A.. "Monodromy in perturbed {K}epler systems: hydrogen atom in crossed fields". Europhysics Letters 47.1 (1999): 1-7. Print.
  • Cushman, Richard. "Routh's sphere". Rep. Math. Phys. 42.1-2 (1998): 47-70. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint". Rep. Math. Phys. 41.1 (1998): 133-142. Print.
  • Beukers, F. and Cushman, Richard. "Zeeman's monotonicity conjecture". J. Differential Equations 143.1 (1998): 191-200. Print.
  • Cushman, Richard and Duistermaat, J. J.. "A characterization of the {L}igon-{S}chaaf regularization map". Communications on Pure and Applied Mathematics 50.8 (1997): 773-787. Print.
  • Cushman, Richard and Bates, Larry. "The magnetic spherical pendulum". Meccanica. International Journal of the Italian Association of Theoretical and Applied Mechanics 30.3 (1995): 271-289. Print.
  • Cushman, Richard, Sniatycki, Jedrzej and Bates, Larry. "Geometry of nonholonomic constraints". Rep. Math. Phys. 36.2-3 (1995): 275-286. Print.
  • Cushman, Richard and Sniatycki, Jedrzej. "Local integrability of the mixmaster model". Rep. Math. Phys. 36.1 (1995): 75-89. Print.
  • Bridges, Thomas J. and Cushman, Richard. "Unipotent normal forms for symplectic maps". Physica D. Nonlinear Phenomena 65.3 (1993): 211-241. Print.
  • Ashbaugh, Mark S., Chicone, Carmen C. and Cushman, Richard. "The twisting tennis racket". Journal of Dynamics and Differential Equations 3.1 (1991): 67-85. Print.
  • Cushman, Richard and Sanders, Jan A.. "The constrained normal form algorithm". Celestial Mechanics. An International Journal of Space Dynamics 45.1-3 (1988/89): 181-187. Print.
  • Cushman, Richard and Duistermaat, J. J.. "The quantum mechanical spherical pendulum". American Mathematical Society. Bulletin. New Series 19.2 (1988): 475-479. Print.
  • Cushman, Richard, Sanders, J. A. and White, N.. "Normal form for the {$(2;n)$}-nilpotent vector field, using invariant theory". Physica D. Nonlinear Phenomena 30.3 (1988): 399-412. Print.
  • Billera, L. J., Cushman, Richard and Sanders, J. A.. "The {S}tanley decomposition of the harmonic oscillator". Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae 50.4 (1988): 375-393. Print.
  • Cushman, Richard. "An analysis of the critical inclination problem using singularity theory". Celestial Mechanics. An International Journal of Space Dynamics 42.1-4 (1987/88): 39-51. Print.
  • Meer, J. and Cushman, Richard. "Orbiting dust under radiation pressure". , (1987): 403-414. Print.
  • Cushman, Richard and Sanders, Jan A.. "Splitting algorithm for nilpotent normal forms". Dynamics and Stability of Systems. An International Journal 2.3-4 (1987): 235-246. Print.
  • Meer, Jan and Cushman, Richard. "Correction to: ``{C}onstrained normalization of {H}amiltonian systems and perturbed {K}eplerian motion'' [{Z}. {A}ngew.\ {M}ath.\ {P}hys.\ {\bf 37} (1986), no.\ 3, 402-424; {MR}0846839 (88e:58030)]". Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physiques Appliqu\'ees 37.6 (1986): 931. Print.
  • Meer, Jan and Cushman, Richard. "Constrained normalization of {H}amiltonian systems and perturbed {K}eplerian motion". Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physiques Appliqu\'ees 37.3 (1986): 402-424. Print.
  • Sanders, Jan A. and Cushman, Richard. "Limit cycles in the {J}osephson equation". SIAM Journal on Mathematical Analysis 17.3 (1986): 495-511. Print.
  • Cushman, Richard, Kelley, Al and Ko{\c{c}}ak, H. "Versal normal form at the {L}agrange equilibrium {$L\sb 4$}". J. Differential Equations 64.3 (1986): 340-374. Print.
  • Cushman, Richard and Sanders, J. A.. "A codimension two bifurcation with a third order {P}icard-{F}uchs equation". J. Differential Equations 59.2 (1985): 243-256. Print.
  • Cushman, Richard, Deprit, Andr and Mosak, Richard. "Normal form and representation theory". Journal of Mathematical Physics 24.8 (1983): 2102-2117. Print.
  • Cushman, Richard. "Reduction, {B}rouwer's {H}amiltonian, and the critical inclination". Celestial Mechanics. An International Journal of Space Dynamics 31.4 (1983): 401-429. Print.
  • Cushman, Richard. "Geometry of the energy momentum mapping of the spherical pendulum". Centrum voor Wiskunde en Informatica. Centre for Mathematics and Computer Science. Newsletter, 1 (1983): 4-18. Print.
  • Cushman, Richard and Rod, David L.. "Reduction of the semisimple {$1:1$} resonance". Physica D. Nonlinear Phenomena 6.1 (1982/83): 105-112. Print.
  • Cushman, Richard. "Geometry of the bifurcations of the normalized reduced {H}\'enon-{H}eiles family". Proc. Roy. Soc. London Ser. A 382.1783 (1982): 361-371. Print.
  • Cushman, Richard and Kelley, Al. "Strongly stable real infinitesimally symplectic mappings". J. Differential Equations 31.2 (1979): 200-223. Print.
  • Cushman, Richard. "Corrections to: ``{T}he relationship between the index of a strongly stable periodic linear {H}amiltonian vectorfield and the index of its stability domain'' [{D}uke {M}ath. {J}. {\bf 45} (1978), no. 4, 701-709;\ {MR} 80g:58027]". Duke Mathematical Journal 46.4 (1979): 881-882. Print.
  • Cushman, Richard. "Examples of nonintegrable analytic {H}amiltonian vector fields with no small divisors". Transactions of the American Mathematical Society 238. (1978): 45-55. Print.
  • Cushman, Richard. "The relationship between the index of a strongly stable periodic linear {H}amiltonian vectorfield and the index of its stability domain". Duke Mathematical Journal 45.4 (1978): 701-709. Print.
  • Burgoyne, N. and Cushman, Richard. "Conjugacy classes in linear groups". Journal of Algebra 44.2 (1977): 339-362. Print.
  • Cushman, Richard and Duistermaat, J. J.. "The behavior of the index of a periodic linear {H}amiltonian system under iteration". Advances in Math. 23.1 (1977): 1-21. Print.
  • Burgoyne, N. and Cushman, Richard. "The decomposition of a linear mapping". Linear Algebra and Appl. 8.6 (1974): 515-519. Print.
  • Burgoyne, N. and Cushman, Richard. "Normal forms for real linear {H}amiltonian systems with purely imaginary eigenvalues". Celestial Mechanics. An International Journal of Space Dynamics 8. (1973/74): 435-443. Print.