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In this paper we provide an extension for the method of Discrete LagrangianDescriptors with the purpose of exploring the phase space of unbounded maps.The key idea is to construct a working definition, that builds on the originalapproach introduced in Lopesino et al. (2015), and which relies on stopping theiteration of initial conditions when their orbits leave a certain region in theplane. This criterion is partly inspired by the classical analysis used inDynamical Systems Theory to study the dynamics of maps by means of escape timeplots. We illustrate the capability of this technique to reveal the geometricaltemplate of stable and unstable invariant manifolds in phase space, and alsothe intricate structure of chaotic sets and strange attractors, by applying itto unveil the phase space of a well-known discrete time system, the H\'enonmap.

An Extension of Discrete Lagrangian Descriptors for Unbounded Maps