Mane genericity theorem for differentiable maps

  • Lee, Kyung-Bok (Department of Mathematics, Hoseo University, Asan-Shi, Chung-Nam 337-850)
  • 발행 : 1996.08.01

초록

Smale [16] posed the following question; is having an attracting periodic orbit a generic property for diffeomorphisms of two-sphere $S^2\ulcorner$(A generic property of $f \in Diff(M)$ is one that is true for a Baire set in Diff(M)). Mane[5] and Plykin[13] had an positive answer for Axiom A diffeomorphisms of $S^2$. To explain our theorem, we begin by briefly recalling stability conjecture posed by palis and smale.

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