A note on fixed points of abelian actions in dimension one

DOI10.1090/PROC/14365zbMath1407.37019arXiv1809.01195OpenAlexW2891883226WikidataQ129294559 ScholiaQ129294559MaRDI QIDQ4621374

Jan P. Boroński

Publication date: 12 February 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.01195

zbMATH Keywords

fixed pointcommuting homeomorphisms

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Continua theory in dynamics (37B45) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Index theory for dynamical systems, Morse-Conley indices (37B30)

Related Items (2)

Strongly commuting interval maps ⋮ A Good Question Won’t Go Away: An Example of Mathematical Research

Cites Work

• Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point
• Snake-like continua
• Fixed points of nilpotent actions on
• Dynamics of commuting homeomorphisms of chainable continua
• The Construction of Global Attractors
• Fixed point properties of nilpotent group actions on 1-arcwise connected continua
• A Transitive Map on [0,1 Whose Inverse Limit is the Pseudoarc]
• Commuting Functions with No Common Fixed Point
• On Common Fixed Points of Commuting Continuous Functions on an Interval
• A Fixed Point Theorem for Pseudo-Arcs and Certain Other Metric Continua

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