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

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

References:

Discrete and Continuous Dynamical Systems

Impact factor

Impact factor: 1.100

RIV identification code

RIV/47813059:19610/22:A0000117

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.3934/dcds.2021159

UT WoS

000722663000001

EID Scopus

2-s2.0-85124549669

Keywords in English

Graph map; limit set; mixing; topological entropy

Abstract

In the original language

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.

Cite

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

@article{65302,
   author = {ForysandKrawiec, Magdalena and Hantáková, Jana and Oprocha, Piotr},
   article_location = {Springfield},
   article_number = {3},
   doi = {https://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://doi.org/10.3934/dcds.2021159.

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