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. |
Other formats:
BibTeX
LaTeX
RIS
@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.
|