Maximal chain continuous factor

Noriaki Kawaguchi

doi:10.3934/dcds.2021101

Article Contents

2021, Volume 41, Issue 12: 5915-5942. Doi: 10.3934/dcds.2021101 open access

This issue Previous Article On the number of invariant measures for random expanding maps in higher dimensions Next Article Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations

Maximal chain continuous factor

Noriaki Kawaguchi

Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan

JSPS Research Fellow

Received: June 30, 2020

Revised: April 30, 2021

Early access: June 2021

Published: December 2021

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Abstract

For any continuous self-map of a compact metric space, we define, prove the existence, and give an explicit expression of a maximal chain continuous factor. For the purpose, we exploit a chain proximal relation and its extension. An example is given to illustrate a difference of the two relations. An alternative proof of a result on the odometers and the regular recurrence is given. Also, we provide an example of a calculation of the maximal chain continuous factor for generic homeomorphism of the Cantor set.

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Mathematics Subject Classification: Primary: 37B02; Secondary: 37B05, 37B65.

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