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- W2964321351 abstract "Let $f:S^1times [0,1]to S^1times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $tilde {f}:mathbb{R}times [0,1]rightarrow mathbb{R}times [0,1]$ we have ${rm Fix}(tilde{f})=mathbb{R}times {0}$ and that $tilde{f}$ positively translates points in $mathbb{R}times {1}$. Let $tilde{f}_epsilon $ be the perturbation of $tilde{f}$ by the rigid horizontal translation $(x,y)mapsto (x+epsilon,y)$. We show that for all $epsilon >0$ sufficiently small we have ${rm Fix} (tilde{f}_epsilon)=emptyset $. The proof follows from Ker'ekj'art'o's construction of Brouwer lines for orientation preserving homeomorphisms of the plane with no fixed points. This result turns out to be sharp with respect to the regularity assumption: there exists a diffeomorphism $f$ satisfying all the properties above, except that $f$ is not real-analytic but only smooth, so that the above conclusion is false. Such a map is constructed via generating functions." @default.
- W2964321351 created "2019-07-30" @default.
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- W2964321351 date "2014-01-01" @default.
- W2964321351 modified "2023-10-14" @default.
- W2964321351 title "Persistence of fixed points under rigid perturbations of maps" @default.
- W2964321351 doi "https://doi.org/10.4064/fm227-1-1" @default.
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