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We introduce a new methodology for a fast and reliable discrimination betweenordered and chaotic orbits in multidimensional Hamiltonian systems which wecall the Linear Dependence Index (LDI). The new method is based on the recentlyintroduced theory of the Generalized Alignment Indices (GALI). LDI takesadvantage of the linear dependence (or independence) of deviation vectors of agiven orbit, using the method of Singular Value Decomposition at every timestep of the integration. We show that the LDI produces estimates whichnumerically coincide with those of the GALI method for the same number of $m$deviation vectors, while its main advantage is that it requires considerableless CPU time than GALI especially in Hamiltonian systems of many degrees offreedom

Detecting Order and Chaos by the Linear Dependence Index (LDI) Method