A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

Yonatan Gutman; Lei Jin; Masaki Tsukamoto

doi:10.1007/s10884-018-9653-3

A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

Yonatan Gutman, Lei Jin, Masaki Tsukamoto

Department of Mathematics

Research output: Contribution to journal › Article

Abstract

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 language	English
Pages (from-to)	81-91
Number of pages	11
Journal	Journal of Dynamics and Differential Equations
Volume	31
Issue number	1
DOIs	https://doi.org/10.1007/s10884-018-9653-3
Publication status	Published - Mar 15 2019

Fingerprint

All Science Journal Classification (ASJC) codes

Analysis

Cite this

Gutman, Y., Jin, L., & Tsukamoto, M. (2019). A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem. Journal of Dynamics and Differential Equations, 31(1), 81-91. https://doi.org/10.1007/s10884-018-9653-3

@article{66306e66c03940ebac1425a46db08bd8,

title = "A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem",

abstract = "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).",

author = "Yonatan Gutman and Lei Jin and Masaki Tsukamoto",

year = "2019",

month = "3",

day = "15",

doi = "10.1007/s10884-018-9653-3",

language = "English",

volume = "31",

pages = "81--91",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

AU - Gutman, Yonatan

AU - Jin, Lei

AU - Tsukamoto, Masaki

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).

UR - http://www.scopus.com/inward/record.url?scp=85042615289&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042615289&partnerID=8YFLogxK

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 -

Access to Document

10.1007/s10884-018-9653-3