Dynamics on dendrites with closed endpoint sets

Roth, Samuel

doi:10.1016/j.na.2020.111745

Search citation statements

Order By: Relevance

Paper Sections

Select...

L' Snoha Et Al1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We may assume that End(D) = Y . By [49,Theorem B], there is a continuous map F : D → D such that the restriction of F onto End(D) = Y is G, and every point of D \ End(D) is eventually mapped to one fixed point which also lies in D \ End(D). This clearly implies that the scrambled sets of F coincide with the scrambled sets of G. Hence, (D, F ) is Li-Yorke chaotic but not Li-Yorke ε-chaotic for any ε > 0.…”

Section: L' Snoha Et Almentioning

confidence: 99%

Generic chaos on dendrites

Snoha¹,

Špitalský²,

Takács³

2021

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

We characterize dendrites D such that a continuous selfmap of D is generically chaotic (in the sense of Lasota) if and only if it is generically ${\varepsilon }$ -chaotic for some ${\varepsilon }>0$ . In other words, we characterize dendrites on which generic chaos of a continuous map can be described in terms of the behaviour of subdendrites with non-empty interiors under iterates of the map. A dendrite D belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if D contains neither a copy of the Riemann dendrite nor a copy of the $\omega $ -star).

show abstract

Section: L' Snoha Et Almentioning

confidence: 99%