A note on core decomposition of Mandelbrot set

Yi Yang and Xiao-Ting Yao

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: Every compactum K⊂C^ has a core decomposition DKPC with Peano quotient, which is the finest one among all upper semi-continuous decompositions into sub-continua such that the quotient space is a Peano compactum [14]. The properties of core decomposition can provide information about the topology of K. Each member of DKPC is called an atom of K. In this paper, it is shown that if {x} is an atom of a continuum K⊂C^ then K is locally connected at x; however, the converse is not true. Moreover, we will obtain singleton atoms of the Mandelbrot set M, based on well known points at which M is locally connected.

Keywords: Locally connected; Core decomposition; Atom (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305439

DOI: 10.1016/j.chaos.2020.110147

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