Inverse problem and equivalent contact systems

TL;DR

This paper explores the inverse problem and equivalence of contact Lagrangian systems, introducing extended contact systems and horizontal equivalence to generalize classical symplectic concepts.

Contribution

It introduces the concept of extended contact Lagrangian systems and horizontal equivalence, advancing the understanding of contact systems and their inverse problems.

Findings

Extended contact systems formalize reparametrizations.

Horizontal equivalence generalizes symplectic case.

Results on the inverse problem for extended contact systems.

Abstract

We present several results on the inverse problem and equivalent contactLagrangian systems. These problems naturally lead to consider smooth transformations on the z variable (i.e., reparametrizations of the action). We present the extended contact Lagrangian systems to formalize this notion. With this structure we define horizontal equivalence of Lagrangians, which generalizes the symplectic case. We also present some results on the inverse problem for extended contact systems.