Local convexity for second order differential equations on a Lie algebroid

Marrero Juan Carlos; de Diego David Martín; Martínez Eduardo

doi:10.3934/jgm.2021021

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2021, Volume 13, Issue 3: 477-499. Doi: 10.3934/jgm.2021021

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Local convexity for second order differential equations on a Lie algebroid

1.
ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Departamento de Matemáticas, Estadística e IO, Sección de Matemáticas y Física, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain
2.
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/Nicolás Cabrera 13-15, 28049 Madrid, Spain
3.
Departamento de Matemática Aplicada e IUMA, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Dedicated to the memory of K Mackenzie

Received: March 2021

Early access: August 2021

Published: September 2021

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Abstract

A theory of local convexity for a second order differential equation (${\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\text{sode}}$ is homogeneous quadratic is extensively discussed.

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Mathematics Subject Classification: Primary: 34A26, 34B15; Secondary: 17B66, 22A22.

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References

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