TY - JOUR
T1 - G-index, topological dynamics and the marker property
AU - Tsukamoto, Masaki
AU - Tsutaya, Mitsunobu
AU - Yoshinaga, Masahiko
N1 - Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.
PY - 2022/12
Y1 - 2022/12
N2 - Given an action of a finite group G on a topological space, we can define its index. The G-index roughly measures a size of the given G-space. We explore connections between the G-index theory and topological dynamics. For a fixed-point free dynamical system, we study the ℤp-index of the set of p-periodic points. We find that its growth is at most linear in p. As an application, we construct a free dynamical system which does not have the marker property. This solves a problem which has been open for several years.
AB - Given an action of a finite group G on a topological space, we can define its index. The G-index roughly measures a size of the given G-space. We explore connections between the G-index theory and topological dynamics. For a fixed-point free dynamical system, we study the ℤp-index of the set of p-periodic points. We find that its growth is at most linear in p. As an application, we construct a free dynamical system which does not have the marker property. This solves a problem which has been open for several years.
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U2 - 10.1007/s11856-022-2433-0
DO - 10.1007/s11856-022-2433-0
M3 - Article
AN - SCOPUS:85145387401
SN - 0021-2172
VL - 251
SP - 737
EP - 764
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -