Collinear Fractals and Bandt’s Conjecture

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	Collinear Fractals and Bandt’s Conjecture
Συγγραφείς:	Bernat Espigule, David Juher, Joan Saldaña
Πηγή:	Fractal and Fractional, Vol 8, Iss 12, p 725 (2024)
Στοιχεία εκδότη:	MDPI AG
Έτος έκδοσης:	2024
Συλλογή:	Directory of Open Access Journals: DOAJ Articles
Θεματικοί όροι:	collinear fractals, Bandt’s conjecture, connectedness locus, iterated function systems, Mandelbrot set, roots of integer polynomials, Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433
Περιγραφή:	For a complex parameter c outside the unit disk and an integer n ≥ 2 , we examine the n-ary collinear fractal E ( c , n ) , defined as the attractor of the iterated function system { f k : C ⟶ C } k = 1 n , where f k ( z ) : = 1 + n − 2 k + c − 1 z . We investigate some topological features of the connectedness locus M n defined as the set of those c for which E ( c , n ) is connected. In particular, we provide a detailed answer to an open question posed by Calegari, Koch, and Walker in 2017. We also extend and refine the technique of the “covering property” by Solomyak and Xu to any n ≥ 2 . We use it to show that a nontrivial portion of M n is regular closed. When n ≥ 21 , we enhance this result by showing that in fact, the whole M n ∖ R lies within the closure of its interior, thus proving that the generalized Bandt’s conjecture is true.
Τύπος εγγράφου:	article in journal/newspaper
Γλώσσα:	English
Relation:	https://www.mdpi.com/2504-3110/8/12/725; https://doaj.org/toc/2504-3110; https://doaj.org/article/22b2fd199b3e4c689fca8e6b15817b49
DOI:	10.3390/fractalfract8120725
Διαθεσιμότητα:	https://doi.org/10.3390/fractalfract8120725 https://doaj.org/article/22b2fd199b3e4c689fca8e6b15817b49
Αριθμός Καταχώρησης:	edsbas.BF45B432
Βάση Δεδομένων:	BASE

View record from BASE

Περιγραφή
DOI:	10.3390/fractalfract8120725