Area-preserving Surface Diffeomorphisms

@inproceedings{Xia2005AreapreservingSD,
  title={Area-preserving Surface Diffeomorphisms},
  author={Zhihong Xia},
  year={2005}
}
We prove some generic properties for C r , r = 1, 2,. .. , ∞, area-preserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [8] on S 2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem. 

From This Paper

Topics from this paper.
4 Citations
26 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 26 references

Topological proofs of some purely topological consequences of carathéodory's theory of prime ends. in Selected Studies

  • J Mather
  • Th. M. Rassias and G. M. Rassias
  • 1982
Highly Influential
8 Excerpts

Les méthodes nouvelles de la mécanique céleste

  • H Poincaré
  • Les méthodes nouvelles de la mécanique céleste
  • 1892
Highly Influential
4 Excerpts

The birkhoff-lewis fixed point theorem and a conjecture of v. i. arnold

  • C Conley, E Zehnder
  • Invent. Math
  • 1983
Highly Influential
3 Excerpts

Closing stable and unstable manifolds on the two-sphere

  • C Robinson
  • Proc. Amer. Math. Soc
  • 1973
Highly Influential
4 Excerpts

Lectures on Celestial Mechanics

  • C L Siegel, J K Moser
  • Lectures on Celestial Mechanics
  • 1971
Highly Influential
3 Excerpts

Generic properties of conservative systems, i, ii

  • C Robinson
  • Amer. J. of Math
  • 1970
Highly Influential
4 Excerpts

On c 1 connecting lemmas

  • L Wen, Z Xia
  • Trans. Amer. Math. Soc
  • 2000

On c ∞ genericity of homoclinic orbits

  • F Oliveira
  • Nonlinearity
  • 2000
3 Excerpts

A basic c 1 perturbation theorem

  • L Wen, Z Xia
  • J. Differential Equations
  • 1999

Similar Papers

Loading similar papers…