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Department of Mathematics and Statistics at the Faculty of Science
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» Larry Bates
Larry Bates
Associate Professor
Applied Mathematics
+1 (403) 220-3942
Mathematical Sciences 428
bates@ucalgary.ca
bates@math.ucalgary.ca
Office Hours
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
1a‑2a
(by appt)
1a‑2a
(by appt)
1a‑2a
(by appt)
1a‑2a
(by appt)
1a‑2a
(by appt)
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Research Interests
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
Currently Teaching
Not currently teaching any courses.
view past courses
Publications
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.
Journal Article
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.
Bates, Larry
.
"
A symmetry completeness criterion for second-order differential equations
"
. Proc. Amer. Math. Soc.
132.6 (2004): 1785-1786 (electronic). 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.
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.
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.
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.
Courses
Degrees
PhD
University of Calgary
, 1988
MA
University of California at Santa Cruz
, 1986
MSc
University of Alberta
, 1984
BSc
Simon Fraser University
, 1979
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