Topological entropy for discontinuous semiflows |
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Authors: | Nelda Jaque Bernado San Martín |
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Institution: | 1. Departamento de Matemáticas, Universidad de Atacama, Copayapu 485, Casilla 240, Copiapó, Chile;2. Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Casilla 1280, Antofagasta, Chile |
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Abstract: | We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to Bowen's ones in the case of continuous semiflows. As a second result, we prove that our entropies give a lower bound for the τ-entropy defined by Alves, Carvalho and Vásquez (2015). Finally, we prove that for impulsive semiflows satisfying certain regularity condition, there exists a continuous semiflow defined on another compact metric space which is related to the first one by a semiconjugation, and whose topological entropy equals our extended notion of topological entropy by using separated sets for the original semiflow. |
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Keywords: | Corresponding author |
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