J 2023

Birkhoff centre and backward limit points

RÝŽOVÁ, Veronika

Basic information

Original name

Birkhoff centre and backward limit points

Authors

RÝŽOVÁ, Veronika (203 Czech Republic, guarantor, belonging to the institution)

Edition

Topology and its Applications, Amsterdam, Elsevier B.V. 2023, 0166-8641

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Topology and its Applications

RIV identification code

RIV/47813059:19610/23:A0000143

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1016/j.topol.2022.108338

UT WoS

000928174900004

Keywords in English

Backward limit points; Birkhoff centre; Dynamical systems; Recurrent points; s alpha-limit sets; beta-limit sets; omega-limit points

Tags

, SGS-16-2022, SGS-18-2019

Tags

International impact, Reviewed
Změněno: 8/4/2024 13:09, Mgr. Aleš Ryšavý

Abstract

V originále

We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps(Hantakova and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of ss-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that ss-limit sets coincide with Birkhoff centre <(Rec(f))over bar> and that the condition for a point to belong to its ss-limit set is equivalent to belonging to the ss-limit set of an other point. In the second part of the paper we deal with genericity of having all s alpha-limit sets closed and we prove that maps with not all s alpha-limit sets closed are dense in C-0([0,1]), which partially solves an open problem also suggested in the aforementioned article.
Displayed: 24/12/2024 13:38