\(C^{0}\) transversality and shadowing properties

DOI10.1134/S0081543807010178zbMath1153.37343OpenAlexW1971502438MaRDI QIDQ2377562

Sergei Yu. Pilyugin, Kazuhiro Sakai

Publication date: 19 January 2009

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543807010178

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

Related Items

Vector fields with the oriented shadowing property ⋮ Rotation set of torus homeomorphisms preserving minimal foliations ⋮ Theory of pseudo-orbit shadowing in dynamical systems ⋮ C¹-stably shadowable chain components ⋮ Weak forms of shadowing in topological dynamics ⋮ Multidimensional \(C^0\) transversality ⋮ Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows ⋮ Sets of dynamical systems with various limit shadowing properties ⋮ C²-stably inverse shadowing diffeomorphisms ⋮ Diffeomorphisms with thes-limit shadowing property ⋮ Shadowing in the case of nontransverse intersection ⋮ Diffeomorphisms with shadowable measures ⋮ Relations between shadowing and inverse shadowing in dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Transversality properties and \(C^1\) open sets of diffeomorphisms with weak shadowing
• On the \(C^ 1\Omega\)-stability conjecture
• Structural stability of diffeomorphisms on two-manifolds
• Stability theorems and hyperbolicity in dynamical systems
• Inverse shadowing by continuous methods
• Shadowing in structurally stable flows
• On Morse-Smale dynamical systems
• Extended f-orbits are approximated by orbits
• Differentiable dynamical systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms