| Contents |
| In this presentation we report new techniques, which we refer to as Lagrangian descriptors, for revealing geometrical structures in phase spaces that are valid for aperiodically time dependent dynamical systems. These are based on the integration, for a finite time, along trajectories of an intrinsic, bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we support their performance by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and several geophysical flows. Comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs), finite size Lyapunov exponents (FSLEs) and finite time averages of certain components of the vector field ("time averages") are carried out. In all cases Lagrangian descriptors are shown to be both more accurate and computationally more efficient than these methods. |
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