Volume-Preserving Diffeomorphisms with the M0 -Shadowing Properties

• Autores: Xinxing Wu, Xu Zhang, Fu Sun
• Localización: Mediterranean journal of mathematics, ISSN 1660-5446, Vol. 18, Nº. 2, 2021
• Idioma: inglés
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• Resumen

  • This paper studies the M0-shadowing property for two types of volume-preserving diffeomorphisms defined on compact manifolds. For symplectic diffeomorphisms defined on symplectic manifolds, the C1-interior of the set of all symplectic diffeomorphisms with the M0-shadowing property is described by the set of the Anosov diffeomorphisms. If a volume-preserving diffeomorphism in Diff1μ(M) is a C1-stable M0-shadowing diffeomorphism, then M admits a volume-hyperbolic dominated splitting.