Generalized Lagrangian Coherent Structures in Finsler Manifolds

TL;DR

This paper extends the concept of Lagrangian Coherent Structures to Finsler manifolds, providing a new geometric framework for analyzing complex dynamical systems in non-Riemannian spaces.

Contribution

It introduces a generalized deformation tensor in Finsler geometry to identify invariant LCS surfaces, broadening the applicability of LCS analysis.

Findings

Existence of invariant LCS surfaces in Finsler manifolds.

Generalization of deformation tensor to non-Riemannian geometries.

Potential applications in astrophysics and fluid dynamics.

Abstract

This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler manifolds. By leveraging Riemannian and Finsler geometry, we generalize the deformation tensor to account for geodesic stretching in these complex spaces. The main result demonstrates the existence of invariant surfaces acting as LCS, characterized by dominant eigenvalues of the generalized deformation tensor. We discuss potential applications in astrophysics, relativistic fluid dynamics, and planetary science. This work paves the way for exploring LCS in intricate geometrical settings, offering new tools for dynamical system analysis.