Abstract
A diffeomorphism f is hyperbolic on a chain-recurrent set if the Morse spectrum does not contain zero. The symbolic image is a directed graph approximating a dynamical system. The chain-recurrent set is localized using this graph. The symbolic image of the differential allows us to estimate the Morse spectrum. A diffeomorphism f is structurally stable if the dual differential has only trivial bounded trajectories. The symbolic image of the dual differential makes it possible to check the absence of bounded trajectories of the dual differential.
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