Irrational rotation factors for conservative torus homeomorphisms
2016 ◽
Vol 37
(5)
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pp. 1537-1546
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Keyword(s):
We provide an equivalent characterization for the existence of one-dimensional irrational rotation factors of conservative torus homeomorphisms that are not eventually annular. It states that an area-preserving non-annular torus homeomorphism $f$ is semiconjugate to an irrational rotation $R_{\unicode[STIX]{x1D6FC}}$ of the circle if and only if there exists a well-defined speed of rotation in some rational direction on the torus, and the deviations from the constant rotation in this direction are uniformly bounded. By means of a counterexample, we also demonstrate that a similar characterization does not hold for eventually annular torus homeomorphisms.
2021 ◽
pp. 014233122110592
Keyword(s):
1984 ◽
Vol 311
(1515)
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pp. 43-102
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Keyword(s):
1986 ◽
Vol 6
(2)
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pp. 205-239
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Keyword(s):
2020 ◽
Vol 37
(4)
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pp. 1447-1467
Keyword(s):
2010 ◽
Vol 31
(4)
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pp. 1193-1228
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2018 ◽
Vol 50
(01)
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pp. 178-203
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2013 ◽
Vol 35
(1)
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pp. 1-33
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Keyword(s):
1997 ◽
Vol 17
(3)
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pp. 575-591
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