A GENERIC PROPERTY FOR DIFFEOMORPHISMSOF THE 2-SPHERE
Citation：
Zhang Zhusheng.A GENERIC PROPERTY FOR DIFFEOMORPHISMSOF THE 2-SPHERE[J].Chinese Annals of Mathematics B,1983,4(1):105~108
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Authors：
Zhang Zhusheng;
Abstract：
S. Sinale posed the following problem as one of “Problems of Present Day Mathematics”:
Is having an attracting periodic orbit (i.e. having a periodic sink or source) a generic
property for diffeomorphisms of the 2-sphere $\[{S^2}\]$?
In this paper, we will prove that having a periodic sink or source is a generic property
for $\[f \in Dif{f^1}({S^2})\]$, and therefore give an affirmative answer to the above Smale's problem.
