On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation Article Swipe

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Nigel P. Byott , Congping Lin , Yiwei Zhang ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1142/s0219493716600133

For an integer [Formula: see text], let [Formula: see text] be the partition of the unit interval [Formula: see text] into [Formula: see text] equal subintervals, and let [Formula: see text] be the class of piecewise linear maps on [Formula: see text] with constant slope [Formula: see text] on each element of [Formula: see text]. We investigate the effect on mixing properties when [Formula: see text] is composed with the interval exchange map given by a permutation [Formula: see text] interchanging the [Formula: see text] subintervals of [Formula: see text]. This extends the work in a previous paper [N. P. Byott, M. Holland and Y. Zhang, DCDS 33 (2013) 3365–3390], where we considered only the “stretch-and-fold” map [Formula: see text].

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Combinatorics

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Mathematics Piecewise Combinatorics Partition (number theory) Interval (graph theory) Unit interval Permutation (music) Constant (computer programming) Mixing (physics) Constant function Piecewise linear function Geometry Mathematical analysis Physics Quantum mechanics Acoustics Programming language Computer science

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Language: en
Landing Page: https://doi.org/10.1142/s0219493716600133
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References: 31
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Title: On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation

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Publication year: 2016

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Authors: Nigel P. Byott, Congping Lin, Yiwei Zhang

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Landing page: https://doi.org/10.1142/s0219493716600133

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Concepts: Mathematics, Piecewise, Combinatorics, Partition (number theory), Interval (graph theory), Unit interval, Permutation (music), Constant (computer programming), Mixing (physics), Constant function, Piecewise linear function, Geometry, Mathematical analysis, Physics, Quantum mechanics, Acoustics, Programming language, Computer science

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abstract_inverted_index.extends	91
abstract_inverted_index.integer	2
abstract_inverted_index.composed	67
abstract_inverted_index.constant	43
abstract_inverted_index.exchange	71
abstract_inverted_index.interval	16, 70
abstract_inverted_index.previous	96
abstract_inverted_index.[Formula:	3, 7, 17, 21, 28, 39, 45, 52, 63, 77, 82, 87, 117
abstract_inverted_index.partition	12
abstract_inverted_index.piecewise	35
abstract_inverted_index.considered	112
abstract_inverted_index.properties	61
abstract_inverted_index.investigate	56
abstract_inverted_index.permutation	76
abstract_inverted_index.subintervals	85
abstract_inverted_index.3365–3390],	109
abstract_inverted_index.interchanging	80
abstract_inverted_index.subintervals,	25
abstract_inverted_index.“stretch-and-fold”	115
cited_by_percentile_year.max	94
cited_by_percentile_year.min	90
countries_distinct_count	2
institutions_distinct_count	3
citation_normalized_percentile.value	0.68592369
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False