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pro vyhledávání: '"Bates, Larry"'
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial Hamiltonian systems.
Externí odkaz:
http://arxiv.org/abs/2402.02560
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This yields an
Externí odkaz:
http://arxiv.org/abs/2108.00280
Autor:
Bates, Larry, Gibson, Peter
We present a riemannian structure on the disk that has a remarkably rich structure. Geodesics are hypocycloids and the (negative of the) laplacian has integer spectrum with multiplicity the Dirichlet divisor function. Eigenfunctions of the laplacian
Externí odkaz:
http://arxiv.org/abs/1603.06622
Autor:
Bates, Larry M., Melko, O. Michael
An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/1507.08939
The elastica is a curve in $\R^3$ that is stationary under variations of the integral of the square of the curvature. Elastica is viewed as a dynamical system that arises from the second order calculus of variations, and its quantization is discussed
Externí odkaz:
http://arxiv.org/abs/1507.01527
Autor:
Bates, Larry, Sniatycki, Jedrzej
The not-quite-Hamiltonian theory of singular reduction and reconstruction is described. This includes the notions of both regular and collective Hamiltonian reduction and reconstruction.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1412.1500
Autor:
Bates, Larry, Sniatycki, Jedrzej
Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.
Comment: 30 pages
Comment: 30 pages
Externí odkaz:
http://arxiv.org/abs/1307.5127
Autor:
Bates, Larry, Sniatycki, Jedrzej
Based mainly on examples of interest in mechanics, we define the notion of a polite group action. One may view this as not only trying to give a more general notion than properness of a group action, but also to more fully understand the role of inva
Externí odkaz:
http://arxiv.org/abs/1305.2465
Autor:
BATES, LARRY, GIBSON, PETER
Publikováno v:
Proceedings of the American Mathematical Society, 2017 Jan 01. 145(1), 461-465.
Externí odkaz:
https://www.jstor.org/stable/procamermathsoci.145.1.461
Autor:
Bates, Larry M., Śniatycki, Jędrzej
Publikováno v:
In Reports on Mathematical Physics August 2015 76(1):41-52