A core decomposition of compact sets in the plane

DOI10.1016/j.aim.2018.11.013zbMath1453.37020arXiv1712.06300OpenAlexW2963798527WikidataQ128861582 ScholiaQ128861582MaRDI QIDQ1711912

Jun Luo, Benoît Loridant, Yi Yang

Publication date: 18 January 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.06300

zbMATH Keywords

locally connectedcore decompositionfinitely SuslinianPeano compactum

Mathematics Subject Classification ID

Compactness (54D30) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Quotient spaces, decompositions in general topology (54B15) Dimension theory in general topology (54F45) Continua theory in dynamics (37B45)

Related Items (3)

A note on core decomposition of Mandelbrot set ⋮ On continuous extension of conformal homeomorphisms of infinitely connected circle domains ⋮ On the lambda function and a quantification of Torhorst theorem

Cites Work

• A numerical scale for non-locally connected planar continua
• Locally connected models for Julia sets
• Boundary local connectivity of tiles in \(\mathbb R^2\)
• Real laminations and the topological dynamics of complex polynomials
• Non-degenerate locally connected models for plane continua and Julia sets
• Irreducible Julia sets of rational functions
• Backward stability for polynomial maps with locally connected Julia sets
• On the boundary connectedness of connected tiles
• Finitely Suslinian models for planar compacta with applications to Julia sets
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