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Two problems in sub-Riemannian geometry.

Shanbrom, Corey R.

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Two problems in sub-Riemannian geometry.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Two problems in sub-Riemannian geometry./
Author:	Shanbrom, Corey R.
Description:	84 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
Contained By:	Dissertation Abstracts International74-11B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3589361
ISBN:	9781303278921

Two problems in sub-Riemannian geometry.
Shanbrom, Corey R.

Two problems in sub-Riemannian geometry. - 84 p.

Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.

Thesis (Ph.D.)--University of California, Santa Cruz, 2013.

In this thesis we study two interesting problems in sub-Riemannian geometry. First, we pose and partially solve the Kepler Problem on the Heisenberg Group. Second, we present a formula for computing the Puiseux characteristic corresponding to a Goursat germ with prescribed small growth vector.

ISBN: 9781303278921Subjects--Topical Terms:

515831
Mathematics.

Two problems in sub-Riemannian geometry.
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020 $a 9781303278921
035 $a (MiAaPQ)AAI3589361
035 $a AAI3589361
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100 1 $a Shanbrom, Corey R. $3 2096795
245 1 0 $a Two problems in sub-Riemannian geometry.
300 $a 84 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
500 $a Adviser: Richard Montgomery.
502 $a Thesis (Ph.D.)--University of California, Santa Cruz, 2013.
520 $a In this thesis we study two interesting problems in sub-Riemannian geometry. First, we pose and partially solve the Kepler Problem on the Heisenberg Group. Second, we present a formula for computing the Puiseux characteristic corresponding to a Goursat germ with prescribed small growth vector.
520 $a The Kepler Problem is among the oldest and most fundamental problems in mechanics. It has been studied in curved geometries, such as the sphere and hyperbolic plane. Here, we formulate the problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg sub-Laplacian. We record many interesting properties of the system, prove the existence of periodic orbits, deduce a version of Kepler's third law, and reduce the integration of a fundamental integrable subsystem to the parametrization of a family of algebraic plane curves.
520 $a Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean and Mormul have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii have shown that such germs correspond to finite jets of Legendrian curve germs, and that the RVT coding corresponds to the classical invariant in the singularity theory of planar curves: the Puiseux characteristic. Here we derive a simple formula for the Puiseux characteristic of the curve corresponding to a Goursat germ with given small growth vector.
590 $a School code: 0036.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a University of California, Santa Cruz. $b Mathematics. $3 2096796
773 0 $t Dissertation Abstracts International $g 74-11B(E).
790 $a 0036
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3589361