Open AccessLocal convexity for second order differential equations on a Lie algebroid
Author(s) -
Juan Carlos Marrero,
David Martı́n de Diego,
Eduardo Martínez
Publication year - 2021
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.511
H-Index - 17
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2021021
Subject(s) - convexity , order (exchange) , homogeneous , quadratic equation , mathematics , differential (mechanical device) , differential equation , pure mathematics , mathematical analysis , combinatorics , geometry , physics , finance , financial economics , economics , thermodynamics
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.