Strong Transitivity and Graph Maps

Katsuya Yokoi

Bulletin of the Polish Academy of Sciences. Mathematics (2005)

  • Volume: 53, Issue: 4, page 377-388
  • ISSN: 0239-7269

Abstract

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We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of f k is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.

How to cite

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Katsuya Yokoi. "Strong Transitivity and Graph Maps." Bulletin of the Polish Academy of Sciences. Mathematics 53.4 (2005): 377-388. <http://eudml.org/doc/281000>.

@article{KatsuyaYokoi2005,
abstract = {We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of $f^\{k\}$ is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.},
author = {Katsuya Yokoi},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {transitive; strongly transitive; graph},
language = {eng},
number = {4},
pages = {377-388},
title = {Strong Transitivity and Graph Maps},
url = {http://eudml.org/doc/281000},
volume = {53},
year = {2005},
}

TY - JOUR
AU - Katsuya Yokoi
TI - Strong Transitivity and Graph Maps
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2005
VL - 53
IS - 4
SP - 377
EP - 388
AB - We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of $f^{k}$ is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.
LA - eng
KW - transitive; strongly transitive; graph
UR - http://eudml.org/doc/281000
ER -

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