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Periodic orbits and fixed points of a $$C^ 1$$ orientation-preserving embedding of $$D^ 2$$. (English) Zbl 0711.57019
Summary: We prove that any periodic orbit $${\mathcal O}$$ of a $$C^ 1$$ orientation- preserving embedding f of the 2-disc $$D^ 2$$ is linked with a fixed point $${\mathcal P}$$ in the sense that the corresponding periodic orbits $$\{\Phi_ t({\mathcal O})\}_{t\geq 0}$$ and $$\{\Phi_ t({\mathcal P})\}_{t\geq 0}$$ of any torus flow $$\Phi_ t$$ suspending f are linked as knots in $$S^ 3$$.

##### MSC:
 57R40 Embeddings in differential topology 37G99 Local and nonlocal bifurcation theory for dynamical systems 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57N05 Topology of the Euclidean $$2$$-space, $$2$$-manifolds (MSC2010)
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##### References:
 [1] DOI: 10.1090/S0273-0979-1988-15685-6 · Zbl 0674.57008 · doi:10.1090/S0273-0979-1988-15685-6 [2] DOI: 10.1007/BFb0061407 · doi:10.1007/BFb0061407 [3] Gambaudo, Ann. Inst. H. Poincar? Phys. Th?or
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