Year: 2015
Type: article
Abstract: In this paper we study the set of Li–Yorke d -tuples and its d -dimensional Lebesgue measure for interval maps T : [0, 1] → [0, 1]. If a topologically mixing T preserves an absolutely continuous probability measure (with respect to Lebesgue), then the d -tuples have Lebesgue full measure, but if T preserves an infinite absolutely continuous measure, the situation becomes more interesting. Taking the family of Manneville–Pomeau maps as an example, we show that for any d ⩾ 2, it is possible that the set of Li–Yorke d -tuples has full Lebesgue measure, but the set of Li–Yorke ( d + 1)-tuples has zero Lebesgue measure.
Source: Nonlinearity
Authors: Henk Bruin, Piotr Oprocha
Institutions: University of Vienna, AGH University of Krakow
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2240472140