TY - JOUR
T1 - A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem
AU - Gutman, Yonatan
AU - Jin, Lei
AU - Tsukamoto, Masaki
N1 - Funding Information:
Y.G. was partially supported by the NCN (National Science Center, Poland) grant 2016/22/E/ST1/00448 and the Marie Curie grant PCIG12-GA-2012-334564. Y.G. and L.J. were partially supported by the National Science Center (Poland) Grant 2013/08/A/ST1/00275. M.T. was supported by John Mung Program of Kyoto University.
Funding Information:
This paper was written when the third named author stayed in the Einstein Institute of Mathematics in the Hebrew University of Jerusalem. He would like to thank the institute for its hospitality.
Publisher Copyright:
© 2018, The Author(s).
PY - 2019/3/15
Y1 - 2019/3/15
N2 - 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).
AB - 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).
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U2 - 10.1007/s10884-018-9653-3
DO - 10.1007/s10884-018-9653-3
M3 - Article
AN - SCOPUS:85042615289
VL - 31
SP - 81
EP - 91
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
IS - 1
ER -