Larry Bates

• My research interests are in the general areas of global Analysis and Differential Geometry, and more specifically in applications of modern analysis to questions in Hamiltonian mechanics and Differential Geometry
• We are continuing the study of Hamiltonian systems with nonholonomic constraints.
• Reduction theory

Book

• Cushman, Richard and Bates, Larry. Global aspects of classical integrable systems Birkh\"auser Verlag, 1997. xvi+435. Print.
• Bates, Larry. An exotic symplectic {${\bf R}\sp 4$} Univ. Montr\'eal, 1990. 33-37. Print.

Conference Proceedings

• Bates, Larry and R. Cushman, M. Hamilton, J. Sniatycki. Decomposition of the quantization representation of an SU(2) action 2009.

Journal Article

• Bates, Larry, Fasso, Francesco and Sansonetto, Nicola. "The Hamilton-Jacobi equation, integrability, and nonholonomic systems". Journal of geometric mechanics 6. (2015): 441-449. Print.
• Bates, Larry and O. M. Melko. "Curves of constant torsion I". Journal of geometry 104. (2013): 213-227. Print.
• Bates, Larry. "A `Big Mac' index for academics". European journal of higher education 3. (2013): 295-296. Print.
• Bates, Larry and J. Sniatycki. "An extension of the Dirac theory of constraints". Journal of fixed point theory and applications 14. (2013): 527-554. Print.
• Bates, Larry and R. Cushman. "Applications of the odd symplectic group in Hamiltonian systems". Regualr and chaotic dynamics 16. (2011): 2-16. Print.
• Bates, Larry and J. Nester. "On D'Alembert's principle". Communications in mathematics 19. (2011): 57-72. Print.
• Bates, Larry and R. Cushman, M. Hamilton, J. Sniatycki. "Quantization of singular reduction". Reviews in mathematical physics 21.3 (2009): 315-371. Print.
• Bates, Larry. "On the linear connection of a second order equation". Journal of geometry and topology 9.3 (2009): 209-213. Print.
• Bates, Larry and R. Cushman. "Scattering monodromy and the A1 singularity". Central european journal of mathematics 5.3 (2007): 429-451. Print.
• Bates, Larry and F. Fasso. "The conjugate locus for the Euler top I. The axisymmetric case". International mathematical forum 2.43 (2007): 2109-2139. Print.
• Bates, Larry. "A smooth invariant not a smooth function of the invariant polynomials". Proceedings of the American mathematical society 135.10 (2007): 3039-3040. Print.
• Bates, Larry and F. Fasso. "An affine model for the actions in an integrable system with monodromy". Regualr and chaotic dynamics 12.5 (2007): 545-549. Print.
• Bates, Larry and M. Winnewisser, B. Winnewisser, I. Medvedev, F. De Lucia, S. Ross. "The hidden kernel of molecular quasi-linearity: Quantum monodromy". Journal of molecular structure 798. (2006): 1-26. Print.
• Bates, Larry. "On the completeness of pseudo-Riemannian metrics". Far east journal of mathematical sciences 18.2 (2005): 155-167. Print.
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  Bates, Larry and Cushman, Richard. "Complete integrability beyond {L}iouville-{A}rnol\cprime d". Rep. Math. Phys. 56.1 (2005): 77-91. Print.
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  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.
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  Bates, Larry and Cushman, Richard. "Removing the cocycle in a momentum map". JP Journal of Geometry and Topology 5.2 (2005): 103-107. Print.
• Bates, Larry. "A symmetry completeness criterion for second-order differential equations". Proc. Amer. Math. Soc. 132.6 (2004): 1785-1786 (electronic). Print.
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  Bates, Larry and Cushman, Richard. "The odd symplectic group in geometry". International Journal of Pure and Applied Mathematics 17.1 (2004): 1-8. Print.
• Bates, Larry. "Problems and progress in nonholonomic reduction". Rep. Math. Phys. 49.2-3 (2002): 143-149. Print.
• Bates, Larry. "A weak counterexample to the {C}arath\'eodory conjecture". Differential Geometry and its Applications 15.1 (2001): 79-80. Print.
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  Bates, Larry and Cushman, Richard. "What is a completely integrable nonholonomic dynamical system?". Rep. Math. Phys. 44.1-2 (1999): 29-35. Print.
• Bates, Larry. "Examples of singular nonholonomic reduction". Rep. Math. Phys. 42.1-2 (1998): 231-247. Print.
• Bates, Larry. "You can't get there from here". Differential Geometry and its Applications 8.3 (1998): 273-274. Print.
• Bates, Larry and Lerman, E.. "Proper group actions and symplectic stratified spaces". Pacific Journal of Mathematics 181.2 (1997): 201-229. Print.
• Sniatycki, Jedrzej, Schwarz, G and Bates, Larry. "Yang-{M}ills and {D}irac fields in a bag, constraints and reduction". Comm. Math. Phys. 176.1 (1996): 95-115. Print.
• Bates, Larry, Graumann, Hugo and MacDonnell, Creighton. "Examples of gauge conservation laws in nonholonomic systems". Rep. Math. Phys. 37.3 (1996): 295-308. 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.
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  Cushman, Richard, Sniatycki, Jedrzej and Bates, Larry. "Geometry of nonholonomic constraints". Rep. Math. Phys. 36.2-3 (1995): 275-286. Print.
• Bates, Larry and Sniatycki, Jedrzej. "Nonholonomic reduction". Rep. Math. Phys. 32.1 (1993): 99-115. Print.
• Bates, Larry and Zou, Maorong. "Degeneration of {H}amiltonian monodromy cycles". Nonlinearity 6.2 (1993): 313-335. Print.
• Bates, Larry and Sniatycki, Jedrzej. "On the period-energy relation". Proc. Amer. Math. Soc. 114.3 (1992): 877-878. Print.
• Bates, Larry and Sniatycki, Jedrzej. "On action-angle variables". Archive for Rational Mechanics and Analysis 120.4 (1992): 337-343. Print.
• Bates, Larry. "Monodromy in the champagne bottle". Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physique Appliqu\'ees 42.6 (1991): 837-847. Print.
• Bates, Larry and Peschke, Georg. "A remarkable symplectic structure". Journal of Differential Geometry 32.2 (1990): 533-538. Print.
• Bates, Larry. "An extension of {L}agrange multipliers". Applicable Analysis. An International Journal 36.3-4 (1990): 265-268. Print.
• Bates, Larry. "Geometric quantization of a perturbed {K}epler problem". Rep. Math. Phys. 28.2 (1989): 289-297. Print.
• Bates, Larry. "A symplectic rigidity theorem". Manuscripta Mathematica 66.1 (1989): 109-111. Print.
• Bates, Larry and Montgomery, Richard. "Closed geodesics on the space of stable two-monopoles". Comm. Math. Phys. 118.4 (1988): 635-640. Print.
• Bates, Larry. "Symmetry preserving deformations of the {K}epler problem". Rep. Math. Phys. 26.3 (1988): 413-428. Print.
• Bates, Larry. "Examples for obstructions to action-angle coordinates". Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 110.1-2 (1988): 27-30. Print.

Preprint

• Bates, Larry. "An inequality for planar elastica.". , (April 2004). Print.
• Bates, Larry and J. Sniatycki. "Not-quite-Hamiltonian reduction". Reports on mathematical physics, (2015). Print.
• Bates, Larry and F. Fasso. "No monodromy in the champagne bottle (and singularities of a superintegrable system)". Journal of geometric mechanics, (2015): 1-15. Print.
• Bates, Larry and J. Sniatycki. "A note on the geometric quantization of angular momentum". Journal of geometry and symmetry in physics, (2015): 1-6. Print.