The local rotation set is an interval
2017 ◽
Vol 38
(7)
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pp. 2571-2617
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Let $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ be the set of all homeomorphisms of the plane that are isotopic to the identity and which fix zero. Recently, in Le Roux [L’ensemble de rotation autour d’un point fixe. Astérisque (350) (2013), 1–109], Le Roux gave the definition of the local rotation set of an isotopy$I$ in $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ from the identity to a homeomorphism $f$ and he asked if this set is always an interval. In this article, we give a positive answer to this question and to the analogous question in the case of the open annulus.
2002 ◽
Vol 132
(1)
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pp. 25-43
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1986 ◽
Vol 38
(4)
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pp. 969-1008
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2018 ◽
Vol 24
(1)
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pp. 211-214
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2003 ◽
Vol 13
(6)
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pp. 799-855
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1979 ◽
Vol 46
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pp. 125-149
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