Symplectic diffeomorphisms and the flux homomorphism

1984 ◽  
Vol 77 (2) ◽  
pp. 353-366 ◽  
Author(s):  
Dusa McDuff
Keyword(s):  
Symplectic Diffeomorphisms ◽  
Flux Homomorphism

scholarly journals A cocycle on the group of symplectic diffeomorphisms

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Światosław R. Gal ◽  
Jarek Kędra
Keyword(s):  
Symplectic Diffeomorphisms

scholarly journals ACrclosing lemma for a class of symplectic diffeomorphisms

Nonlinearity ◽  
2006 ◽  
Vol 19 (2) ◽  
pp. 511-516 ◽  
Author(s):  
Zhihong Xia ◽  
Hua Zhang
Keyword(s):  
Symplectic Diffeomorphisms

scholarly journals On the generic existence of homoclinic points

1987 ◽  
Vol 7 (4) ◽  
pp. 567-595 ◽  
Author(s):  
Fernando Oliveira
Keyword(s):  
Periodic Point ◽  
Invariant Manifolds ◽  
Compact Manifolds ◽  
Homoclinic Points ◽  
Symplectic Diffeomorphisms ◽  
Generic Existence ◽  
Area Preserving ◽  
Orientable Surfaces

AbstractThis work is concerned with the generic existence of homoclinic points for area preserving diffeomorphisms of compact orientable surfaces. We give a shorter proof of Pixton's theorem that shows that, Cr-generically, an area preserving diffeomorphism of the two sphere has the property that every hyperbolic periodic point has transverse homoclinic points. Then, we extend Pixton's result to the torus and investigate certain generic aspects of the accumulation of the invariant manifolds all over themselves in the case of symplectic diffeomorphisms of compact manifolds.

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