On the Lebesgue Measure of Li-Yorke Pairs for Interval Maps |
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| Authors: | Henk Bruin Víctor Jiménez López |
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| Institution: | 1. Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
2. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain
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| Abstract: | We investigate the prevalence of Li-Yorke pairs for C
2 and C
3 multimodal maps f with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly
wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. |
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