A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

Yonatan Gutman, Lei Jin, Masaki Tsukamoto

Research output: Contribution to journalArticle


We prove that an R-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions R→ [0 , 1] if its fixed point set can be topologically embedded in the unit interval. This is a refinement of the classical Bebutov–Kakutani theorem (1968).

Original languageEnglish
Pages (from-to)81-91
Number of pages11
JournalJournal of Dynamics and Differential Equations
Issue number1
Publication statusPublished - Mar 15 2019


All Science Journal Classification (ASJC) codes

  • Analysis

Cite this