Conjugate points for systems of second-order ordinary differential equations
- Author
- S. Hajdu and Tom Mestdag (UGent)
- Organization
- Abstract
- We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a nontrivial Jacobi field along that curve that vanishes on both points. Based on arguments that involve the eigendistributions of the Jacobi endomorphism, we discuss conjugate points for a certain generalization (to the current setting) of locally symmetric spaces. Next, we study conjugate points along relative equilibria of Lagrangian systems with a symmetry Lie group. We end the paper with some examples and applications.
- Keywords
- INVERSE PROBLEM, JACOBI FIELDS, CONNECTIONS, CALCULUS, Second-order ordinary differential equations, Jacobi fields, conjugate, points, symmetry, relative equilibrium
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8710790
- MLA
- Hajdu, S., and Tom Mestdag. “Conjugate Points for Systems of Second-Order Ordinary Differential Equations.” INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol. 17, no. 1, 2020, doi:10.1142/S0219887820500127.
- APA
- Hajdu, S., & Mestdag, T. (2020). Conjugate points for systems of second-order ordinary differential equations. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 17(1). https://doi.org/10.1142/S0219887820500127
- Chicago author-date
- Hajdu, S., and Tom Mestdag. 2020. “Conjugate Points for Systems of Second-Order Ordinary Differential Equations.” INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS 17 (1). https://doi.org/10.1142/S0219887820500127.
- Chicago author-date (all authors)
- Hajdu, S., and Tom Mestdag. 2020. “Conjugate Points for Systems of Second-Order Ordinary Differential Equations.” INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS 17 (1). doi:10.1142/S0219887820500127.
- Vancouver
- 1.Hajdu S, Mestdag T. Conjugate points for systems of second-order ordinary differential equations. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. 2020;17(1).
- IEEE
- [1]S. Hajdu and T. Mestdag, “Conjugate points for systems of second-order ordinary differential equations,” INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol. 17, no. 1, 2020.
@article{8710790,
abstract = {{We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a nontrivial Jacobi field along that curve that vanishes on both points. Based on arguments that involve the eigendistributions of the Jacobi endomorphism, we discuss conjugate points for a certain generalization (to the current setting) of locally symmetric spaces. Next, we study conjugate points along relative equilibria of Lagrangian systems with a symmetry Lie group. We end the paper with some examples and applications.}},
articleno = {{2050012}},
author = {{Hajdu, S. and Mestdag, Tom}},
issn = {{0219-8878}},
journal = {{INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS}},
keywords = {{INVERSE PROBLEM,JACOBI FIELDS,CONNECTIONS,CALCULUS,Second-order ordinary differential equations,Jacobi fields,conjugate,points,symmetry,relative equilibrium}},
language = {{eng}},
number = {{1}},
pages = {{25}},
title = {{Conjugate points for systems of second-order ordinary differential equations}},
url = {{http://doi.org/10.1142/S0219887820500127}},
volume = {{17}},
year = {{2020}},
}
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