On the structure of α-limit sets of backward trajectories for
graph maps

J 2022

On the structure of α-limit sets of backward trajectories for graph maps

FORYS-KRAWIEC, Magdalena, Jana HANTÁKOVÁ and Piotr OPROCHA

Basic information

Original name

On the structure of α-limit sets of backward trajectories for graph maps

Authors

FORYS-KRAWIEC, Magdalena (616 Poland), Jana HANTÁKOVÁ (203 Czech Republic, guarantor, belonging to the institution) and Piotr OPROCHA (203 Czech Republic)

Edition

Discrete and Continuous Dynamical Systems, Springfield, American Institute of Mathematical Sciences, 2022, 1078-0947

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Discrete and Continuous Dynamical Systems

RIV identification code

RIV/47813059:19610/22:A0000117

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.3934/dcds.2021159

UT WoS

000722663000001

Keywords in English

Graph map; limit set; mixing; topological entropy

Abstract

V originále

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.

Citovat

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.

@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.

Detailed Information on Publication Record