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- W1542087700 abstract "We prove that if a symplectic diffeomorphism is not partially hyperbolic, then with an arbitrarily small<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1><mml:semantics><mml:msup><mml:mi>C</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:annotation encoding=application/x-tex>C^1</mml:annotation></mml:semantics></mml:math></inline-formula>perturbation we can create a totally elliptic periodic point inside any given open set. As a consequence, a<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1><mml:semantics><mml:msup><mml:mi>C</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:annotation encoding=application/x-tex>C^1</mml:annotation></mml:semantics></mml:math></inline-formula>-generic symplectic diffeomorphism is either partially hyperbolic or it has dense elliptic periodic points. This extends the similar results of S. Newhouse in dimension 2 and M.-C. Arnaud in dimension 4. Another interesting consequence is that stably ergodic symplectic diffeomorphisms must be partially hyperbolic, a converse to Shub-Pugh’s stable ergodicity conjecture for the symplectic case." @default.
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- W1542087700 date "2006-06-19" @default.
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- W1542087700 title "Partial hyperbolicity or dense elliptic periodic points for 𝐶¹-generic symplectic diffeomorphisms" @default.
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