A shadowing lemma for quasi-hyperbolic strings of flows |
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Authors: | Bo Han Xiao Wen |
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Institution: | The School of Mathematical and System Science, Beihang University, Beijing 100191, China |
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Abstract: | In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article. |
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Keywords: | 37C05 37C10 37C27 37D30 Shadowing property Linear Poincaré flow Dominated splitting Quasi-hyperbolic string Sectional Poincaré map |
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