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Richard Cushman

Adjunct Professor

Publications

Book

Beukers, Frits and Cushman, Richard. The complex geometry of the spherical pendulum 292. Amer. Math. Soc., 2002. 47-70.
Cushman, Richard and Bates, Larry. Global aspects of classical integrable systems Birkh\"auser Verlag, 1997. xvi+435.
Cushman, Richard and Hermans, J. . The rolling disc 19. Birkh\"auser, 1996. 21-60.
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.
Cushman, Richard and Hoveijn, I. . Visualizing special motions of the {E}uler top 4. World Sci. Publ., River Edge, NJ, 1995. 153-167.
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.
Cushman, Richard. Geometry of perturbation theory 332. Plenum, 1994. 89-101.
Cohen, A. M. and Cushman, Richard. Gr\"obner bases and standard monomial theory 109. Birkh\"auser Boston, 1993. 41-60.
Cushman, Richard. A survey of normalization techniques applied to perturbed {K}eplerian systems 1. Springer, 1992. 54-112.
Cushman, Richard and Sjamaar, Reyer . On singular reduction of {H}amiltonian spaces 99. Birkh\"auser Boston, 1991. 114-128.
Arms, Judith M., Cushman, Richard and Gotay, Mark J.. A universal reduction procedure for {H}amiltonian group actions 22. Springer, 1991. 33-51.
Cushman, Richard and Meer, J. . The {H}amiltonian {H}opf bifurcation in the {L}agrange top 1416. Springer, 1990. 26-38.
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.
Cushman, Richard and Sanders, Jan A.. Nilpotent normal form in dimension {$4$} 37. Springer, 1987. 61-66.
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.
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.
Cushman, Richard and Kn{\"o}rrer, H. . The energy momentum mapping of the {L}agrange top 1139. Springer, 1985. 12-24.
Sanders, J. A. and Cushman, Richard. Abelian integrals and global {H}opf bifurcations 1125. Springer, 1985. 87-98.
Cushman, Richard. Normal form for {H}amiltonian vectorfields with periodic flows 6. Reidel, 1984. 125-144.
Cushman, Richard. Periodic solutions of the autonomous {J}osephson equation 985. Springer, 1983. 319-326.
Cushman, Richard. Morse theory and the method of averaging 70. Dekker, 1981. 25-37.
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.
Cushman, Richard. The momentum mapping of the harmonic oscillator Academic Press, 1974. 323-342.

Journal Paper

Efstathiou, K. , Cushman, Richard and Sadovski{\'{\i}}, D. A.. Fractional monodromy in the {$1:-2$} resonance 209.1 2007. 241-273.
Cushman, Richard and Kallen, Wilberd . A new interpretation for the mass of a classical relativistic particle 24.3 2006. 230-234.
Cushman, Richard and Duistermaat, J. J.. Nearly flat falling motions of the rolling disk 11.1 2006. 31-60.
Cushman, Richard and Kallen, Wilberd . Adjoint and coadjoint orbits of the {P}oincar\'e group 90.1-2 2006. 65-89.
Bates, Larry and Cushman, Richard. Complete integrability beyond {L}iouville-{A}rnol\cprime d 56.1 2005. 77-91.
Bates, Larry, Cushman, Richard and Savev, Emil. The rotation number and the herpolhode angle in {E}uler's top 56.2 2005. 183-191.
Bates, Larry and Cushman, Richard. Removing the cocycle in a momentum map 5.2 2005. 103-107.
Dullin, Holger , Giacobbe, Andrea and Cushman, Richard. Monodromy in the resonant swing spring 190.1-2 2004. 15-37.
Efstathiou, K. , Cushman, Richard and Sadovski{\'{\i}}, D. A.. Hamiltonian {H}opf bifurcation of the hydrogen atom in crossed fields 194.3-4 2004. 250-274.
Bates, Larry and Cushman, Richard. The odd symplectic group in geometry 17.1 2004. 1-8.
Giacobbe, A. , Cushman, Richard, Sadovski{\'{\i}}, D. A. and Zhilinski{\'{\i}}, B. I.. Monodromy of the quantum {$1:1:2$} resonant swing spring 45.12 2004. 5076-5100.
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] 55.2 2003. 247.
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)] 55.2 2003. 247.
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 459.2040 2003. 2997-3019.
Cushman, Richard and Sniatycki, Jedrzej. A nonholonomic oscillator 50.1 2002. 85-98.
Cushman, Richard and Sniatycki, Jedrzej. Nonholonomic reduction for free and proper actions 7.1 2002. 61-72.
Cushman, Richard and Zhilinskii, Boris . Monodromy of a two degrees of freedom {L}iouville integrable system with many focus-focus singular points 35.28 2002. L415-L419.
Cushman, Richard. Sign of the monodromy for {L}iouville integrable systems 3.5 2002. 883-894.
Cushman, Richard and Roberts, Mark . Poisson structures transverse to coadjoint orbits 126.7 2002. 525-534.
Cushman, Richard and Sniatycki, Jedrzej. Differential structure of orbit spaces 53.4 2001. 715-755.
Cushman, Richard and Duistermaat, J. J.. Non-{H}amiltonian monodromy 172.1 2001. 42-58.
Cushman, Richard and Sadovski{\'{\i}}, D. A.. Monodromy in the hydrogen atom in crossed fields 142.1-2 2000. 166-196.
Bates, Larry and Cushman, Richard. What is a completely integrable nonholonomic dynamical system? 44.1-2 1999. 29-35.
Cushman, Richard, Ferrer, Sebasti and Han{\ss}mann, Heinz . Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator 12.2 1999. 389-410.
Cushman, Richard and Sniatycki, Jedrzej. Hamiltonian mechanics on principal bundles 21.2 1999. 60-64.
Cushman, Richard and Sadovski{\'{\i}}, D. A.. Monodromy in perturbed {K}epler systems: hydrogen atom in crossed fields 47.1 1999. 1-7.
Cushman, Richard. Routh's sphere 42.1-2 1998. 47-70.
Cushman, Richard and Sniatycki, Jedrzej. A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint 41.1 1998. 133-142.
Beukers, F. and Cushman, Richard. Zeeman's monotonicity conjecture 143.1 1998. 191-200.
Cushman, Richard and Duistermaat, J. J.. A characterization of the {L}igon-{S}chaaf regularization map 50.8 1997. 773-787.
Cushman, Richard and Bates, Larry. The magnetic spherical pendulum 30.3 1995. 271-289.
Cushman, Richard, Sniatycki, Jedrzej and Bates, Larry. Geometry of nonholonomic constraints 36.2-3 1995. 275-286.
Cushman, Richard and Sniatycki, Jedrzej. Local integrability of the mixmaster model 36.1 1995. 75-89.
Bridges, Thomas J. and Cushman, Richard. Unipotent normal forms for symplectic maps 65.3 1993. 211-241.
Ashbaugh, Mark S., Chicone, Carmen C. and Cushman, Richard. The twisting tennis racket 3.1 1991. 67-85.
Cushman, Richard and Sanders, Jan A.. The constrained normal form algorithm 45.1-3 1988/89. 181-187.
Cushman, Richard and Duistermaat, J. J.. The quantum mechanical spherical pendulum 19.2 1988. 475-479.
Cushman, Richard, Sanders, J. A. and White, N. . Normal form for the {$(2;n)$}-nilpotent vector field, using invariant theory 30.3 1988. 399-412.
Billera, L. J., Cushman, Richard and Sanders, J. A.. The {S}tanley decomposition of the harmonic oscillator 50.4 1988. 375-393.
Cushman, Richard. An analysis of the critical inclination problem using singularity theory 42.1-4 1987/88. 39-51.
Meer, J. and Cushman, Richard. Orbiting dust under radiation pressure 1987. 403-414.
Cushman, Richard and Sanders, Jan A.. Splitting algorithm for nilpotent normal forms 2.3-4 1987. 235-246.
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)] 37.6 1986. 931.
Meer, Jan and Cushman, Richard. Constrained normalization of {H}amiltonian systems and perturbed {K}eplerian motion 37.3 1986. 402-424.
Sanders, Jan A. and Cushman, Richard. Limit cycles in the {J}osephson equation 17.3 1986. 495-511.
Cushman, Richard, Kelley, Al and Ko{\c{c}}ak, H . Versal normal form at the {L}agrange equilibrium {$L\sb 4$} 64.3 1986. 340-374.
Cushman, Richard and Sanders, J. A.. A codimension two bifurcation with a third order {P}icard-{F}uchs equation 59.2 1985. 243-256.
Cushman, Richard, Deprit, Andr and Mosak, Richard . Normal form and representation theory 24.8 1983. 2102-2117.
Cushman, Richard. Reduction, {B}rouwer's {H}amiltonian, and the critical inclination 31.4 1983. 401-429.
Cushman, Richard. Geometry of the energy momentum mapping of the spherical pendulum 1 1983. 4-18.
Cushman, Richard and Rod, David L.. Reduction of the semisimple {$1:1$} resonance 6.1 1982/83. 105-112.
Cushman, Richard. Geometry of the bifurcations of the normalized reduced {H}\'enon-{H}eiles family 382.1783 1982. 361-371.
Cushman, Richard and Kelley, Al . Strongly stable real infinitesimally symplectic mappings 31.2 1979. 200-223.
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] 46.4 1979. 881-882.
Cushman, Richard. Examples of nonintegrable analytic {H}amiltonian vector fields with no small divisors 238. 1978. 45-55.
Cushman, Richard. The relationship between the index of a strongly stable periodic linear {H}amiltonian vectorfield and the index of its stability domain 45.4 1978. 701-709.
Burgoyne, N. and Cushman, Richard. Conjugacy classes in linear groups 44.2 1977. 339-362.
Cushman, Richard and Duistermaat, J. J.. The behavior of the index of a periodic linear {H}amiltonian system under iteration 23.1 1977. 1-21.
Burgoyne, N. and Cushman, Richard. The decomposition of a linear mapping 8.6 1974. 515-519.
Burgoyne, N. and Cushman, Richard. Normal forms for real linear {H}amiltonian systems with purely imaginary eigenvalues 8. 1973/74. 435-443.

$Photograph of Richard Cushman$

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