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C<sup>1</sup>-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOV
Bessa, Mario Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
In this short note we prove that if a symplectomorphism $f$ is $C^1$-stably shadowable, then $f$ is Anosov. The same result is obtained for volume-preserving diffeomorphisms.
C1-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOV
Mario Bessa 대한수학회 2013 대한수학회보 Vol.50 No.5
In this short note we prove that if a symplectomorphism f is C1-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.
STABLE WEAK SHADOWABLE SYMPLECTOMORPHISMS ARE PARTIALLY HYPERBOLIC
Bessa, Mario,Vaz, Sandra Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.2
Let M be a closed, symplectic connected Riemannian manifold and f a symplectomorphism on M. We prove that if f is $C^1$-stably weak shadowable on M, then the whole manifold M admits a partially hyperbolic splitting.