Abstract
We show that the map part of the discrete Conley index carries information which can be used to detect the existence of connections in the repeller-attractor decomposition of an isolated invariant set of a homeomorphism. We use this information to provide a characterization of invariant sets which admit a semi-conjugacy onto the space of sequences on K symbols with dynamics given by a subshift. These ideas are applied to the Henon map to prove the existence of chaotic dynamics on an open set of parameter values.
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Research funded in part by NSF Grant DMS-9101412.
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Mischaikow, K., Mrozek, M. Isolating neighborhoods and chaos. Japan J. Indust. Appl. Math. 12, 205–236 (1995). https://doi.org/10.1007/BF03167289
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DOI: https://doi.org/10.1007/BF03167289