A study was conducted to analyze the sets of vector fields with various shadowing properties of pseudotrajectories. The main difference between the shadowing problem for flows and a similar problem for discrete dynamical systems generated by diffeomorphisms is related to the necessity of reparameterization of shadowing trajectories in the former case. The aim of the study is also to describe the structure of C1 interiors of sets of vector fields with various shadowing properties. A monotonically increasing homeomorphism h of the line R such as h(0) = 0 is called a reparameterization. The study analyzed that a field X has the Lipschitz shadowing property if there exist certain numbers with particular properties. The study also concludes that a field X has the orbital shadowing property if there exists a number with a particular property.

Original languageEnglish
Pages (from-to)669-670
Number of pages2
JournalDoklady Mathematics
Volume78
Issue number2
DOIs
StatePublished - 1 Oct 2008

    Scopus subject areas

  • Mathematics(all)

ID: 43393237