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The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. (English) Zbl 1311.76109

Summary: We generalize the concepts of finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures to arbitrary Riemannian manifolds. The methods are illustrated for convection cells on cylinders and Möbius strips, as well as for the splitting of the Antarctic polar vortex in the spherical stratosphere and a related point vortex model. We modify the FTLE computational method and accommodate unstructured meshes of triangles and tetrahedra to fit manifolds of arbitrary shape, as well as to facilitate dynamic refinement of the FTLE mesh.{
©2010 American Institute of Physics}

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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