# American Institute of Mathematical Sciences

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

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.

Citation: Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez. Local convexity for second order differential equations on a Lie algebroid. Journal of Geometric Mechanics, doi: 10.3934/jgm.2021021
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##### References:
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