Symmetries of second order differential equations on Lie algebroids

TL;DR

This paper explores the geometric symmetries of second order differential equations within the framework of Lie algebroids, linking various structures like semisprays and connections to understand their properties.

Contribution

It introduces a comprehensive geometric approach to analyze symmetries of second order differential equations on Lie algebroids, extending classical methods.

Findings

Established relations between semisprays, connections, and Jacobi endomorphisms on Lie algebroids.

Characterized symmetries of second order differential equations using geometric structures.

Provided a unified framework for studying differential equations on Lie algebroids.

Abstract

In this paper we investigate the relations between semispray, nonlinear connection, dynamical covariant derivative and Jacobi endomorphism on Lie algebroids. Using these geometric structures, we study the symmetries of second order differential equations in the general framework of Lie algebroids.