Generalized Lagrangian Coherent Structures in Finsler Manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912184053792768 |
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| author | Santos, Rômulo Damasclin Chaves dos Sales, Jorge Henrique de Oliveira |
| author_facet | Santos, Rômulo Damasclin Chaves dos Sales, Jorge Henrique de Oliveira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Lagrangian Coherent Structures in Finsler Manifolds Santos, Rômulo Damasclin Chaves dos Sales, Jorge Henrique de Oliveira General Mathematics 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. |
| title | Generalized Lagrangian Coherent Structures in Finsler Manifolds |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2501.06198 |