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Sensitivity and historic behavior for continuous maps on Baire metric spaces
Published online by Cambridge University Press: 07 February 2023
Abstract
We introduce a notion of sensitivity with respect to a continuous real-valued bounded map which provides a sufficient condition for a continuous transformation, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic behavior (also known as irregular points). The applications of this criterion recover, and extend, several known theorems on the genericity of the irregular set, in addition to yielding a number of new results, including information on the irregular set of geodesic flows, in both negative and non-positive curvature, and semigroup actions.
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- © The Author(s), 2023. Published by Cambridge University Press
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