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Separatrices, manifolds of hyperbolic saddles, and tumultuous seas of dynamical systems can be found in scalar quantities suitable to reveal Lagrangian Descriptors. For 1-degree-of-freedom Hamiltonian systems, we introduce and exploit an intrinsic geometrical parametrisation of LDs, which is unaffected by the time. The parametrization method is purely dependent on the system's energy supply and the geometry of the associated level curve. Regardless of the dynamical framework, the same power laws of divergence are found for the problems investigated. Some of our findings are similar to existing estimates obtained with temporal LDs under approximations.
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