Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 893-917 |
| Seitenumfang | 25 |
| Fachzeitschrift | Journal of Nonlinear and Convex Analysis |
| Jahrgang | 18 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - 2017 |
Abstract
We discuss the complete integrability of the bi-characteristic flows of a sub-Laplacian and its related Grushin type operator. In many cases, first integrals will be given by homogeneous functions, so that we treat the problem of the complete integrability in the framework of pseudo-differential operators and show some examples of first integrals given as principal symbols of quasi-commuting operators. Explicit examples of the general theory are provided and we present first integrals for left invariant sub-Laplacians corresponding to three sub-Riemannian structures on SX(2,ℝ) and related Grushin type operators on nine left coset spaces. In the last three sections we treat sub-Laplacians on S3, Heisenberg and Engel groups.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Steuerung und Optimierung
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of Nonlinear and Convex Analysis, Jahrgang 18, Nr. 5, 2017, S. 893-917.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - First integrals of bi-characteristic curves of a sub-Laplacian and related Grushin type operators
AU - Bauer, Wolfram
AU - Furutani, Kenro
AU - Tamura, Mitsuji
N1 - Funding Information: The second named author was partially supported by the National Center for Theoretical Science, National Taiwan University Taipei and China Medical University, Taichung, Taiwan. Publisher Copyright: © 2017. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - We discuss the complete integrability of the bi-characteristic flows of a sub-Laplacian and its related Grushin type operator. In many cases, first integrals will be given by homogeneous functions, so that we treat the problem of the complete integrability in the framework of pseudo-differential operators and show some examples of first integrals given as principal symbols of quasi-commuting operators. Explicit examples of the general theory are provided and we present first integrals for left invariant sub-Laplacians corresponding to three sub-Riemannian structures on SX(2,ℝ) and related Grushin type operators on nine left coset spaces. In the last three sections we treat sub-Laplacians on S3, Heisenberg and Engel groups.
AB - We discuss the complete integrability of the bi-characteristic flows of a sub-Laplacian and its related Grushin type operator. In many cases, first integrals will be given by homogeneous functions, so that we treat the problem of the complete integrability in the framework of pseudo-differential operators and show some examples of first integrals given as principal symbols of quasi-commuting operators. Explicit examples of the general theory are provided and we present first integrals for left invariant sub-Laplacians corresponding to three sub-Riemannian structures on SX(2,ℝ) and related Grushin type operators on nine left coset spaces. In the last three sections we treat sub-Laplacians on S3, Heisenberg and Engel groups.
KW - Bi-characteristic flow
KW - Completely integral system
KW - Geodesic flow
KW - Grushin type operator
KW - Pseudo-differential operator
KW - Sub-Riemannian structure
UR - http://www.scopus.com/inward/record.url?scp=85026804696&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85026804696
VL - 18
SP - 893
EP - 917
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
SN - 1345-4773
IS - 5
ER -