| FORYS-KRAWIEC, Magdalena, Jana HANTÁKOVÁ and Piotr OPROCHA. On the structure of α-limit sets of backward trajectories for graph maps. Discrete and Continuous Dynamical Systems. Springfield: American Institute of Mathematical Sciences, 2022, vol. 42, No 3, p. 1435-1463. ISSN 1078-0947. Available from: https://dx.doi.org/10.3934/dcds.2021159. |
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@article{65302,
author = {ForysandKrawiec, Magdalena and Hantáková, Jana and Oprocha, Piotr},
article_location = {Springfield},
article_number = {3},
doi = {http://dx.doi.org/10.3934/dcds.2021159},
keywords = {Graph map; limit set; mixing; topological entropy},
language = {eng},
issn = {1078-0947},
journal = {Discrete and Continuous Dynamical Systems},
title = {On the structure of α-limit sets of backward trajectories for graph maps},
url = {https://www.aimsciences.org/article/doi/10.3934/dcds.2021159},
volume = {42},
year = {2022}
}
TY - JOUR
ID - 65302
AU - Forys-Krawiec, Magdalena - Hantáková, Jana - Oprocha, Piotr
PY - 2022
TI - On the structure of α-limit sets of backward trajectories for graph maps
JF - Discrete and Continuous Dynamical Systems
VL - 42
IS - 3
SP - 1435-1463
EP - 1435-1463
PB - American Institute of Mathematical Sciences
SN - 10780947
KW - Graph map
KW - limit set
KW - mixing
KW - topological entropy
UR - https://www.aimsciences.org/article/doi/10.3934/dcds.2021159
N2 - In the paper we study what sets can be obtained as alpha-limit sets of backward trajectories in graph maps. We show that in the case of mixing maps, all those alpha-limit sets are omega-limit sets and for all but finitely many points x, we can obtain every omega-limits set as the alpha-limit set of a backward trajectory starting in x. For zero entropy maps, every alpha-limit set of a backward trajectory is a minimal set. In the case of maps with positive entropy, we obtain a partial characterization which is very close to complete picture of the possible situations.
ER -
FORYS-KRAWIEC, Magdalena, Jana HANTÁKOVÁ and Piotr OPROCHA. On the structure of α-limit sets of backward trajectories for graph maps. \textit{Discrete and Continuous Dynamical Systems}. Springfield: American Institute of Mathematical Sciences, 2022, vol.~42, No~3, p.~1435-1463. ISSN~1078-0947. Available from: https://dx.doi.org/10.3934/dcds.2021159.
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