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Transversal homoclinic points and hyperbolic sets for non-autonomous maps I

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Abstract

A concept of generalized hyperbolic sets for non-autonomous maps is developed. Starting from transversal homoclinic orbits such generalized hyperbolic sets are constructed. The Shadowing Lemma is proven for maps admitting a generalized hyperbolic set. Time dependent symbolic dynamics is introduced and related to non-autonomous maps.

Zusammenfassung

Das Konzept von verallgemeinerten hyperbolischen Mengen für nicht-autonome Abbildungen wird entwickelt. Ausgehend von transversalen homoklinen Bahnen werden solche verallgemeinerte hyperbolische Mengen konstruiert. Das Shadowing Lemma wird für Abbildungen bewiesen, welche eine verallgemeinerte hyperbolische Menge haben. Es wird zeitabhängige symbolische Dynamik eingeführt und der Zusammenhang mit nicht-autonomen Abbildungen dargestellt.

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Stoffer, D. Transversal homoclinic points and hyperbolic sets for non-autonomous maps I. Z. angew. Math. Phys. 39, 518–549 (1988). https://doi.org/10.1007/BF00948961

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