Relative entropy, asymptotic pairs and chaos

• Autores: Guohua Zhang
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 73, Nº 1, 2006, págs. 157-172
• Idioma: inglés
• DOI: 10.1112/s0024610705022520
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• Resumen

  • In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.