Local convexity for second order differential equations on a Lie algebroid
Juan Carlos Marrero, David Mart\'in de Diego, Eduardo Mart\'inez
TL;DR
This paper develops a theory of local convexity for second order differential equations on Lie algebroids, with detailed analysis for the special case of homogeneous quadratic SODEs.
Contribution
It introduces a novel framework for local convexity in the context of Lie algebroids and explores the properties of quadratic SODEs within this framework.
Findings
Established local convexity conditions for SODEs on Lie algebroids.
Analyzed the specific case of homogeneous quadratic SODEs.
Provided insights into the geometric structure of solutions.
Abstract
A theory of local convexity for a second order differential equation (SODE) on a Lie algebroid is developed. The particular case when the SODE is homogeneous quadratic is extensively discussed.
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