On Rational Functions Sharing the Measure of Maximal Entropy

On Rational Functions Sharing the Measure of Maximal Entropy We show that describing rational functions f1,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f_1,$$\end{document}f2,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f_2,$$\end{document}⋯,fn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\dots ,f_n$$\end{document} sharing the measure of maximal entropy reduces to describing solutions of the functional equation A∘X1=A∘X2=⋯=A∘Xn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A\circ X_1=A\circ X_2=\dots =A\circ X_n$$\end{document} in rational functions. We also provide some results about solutions of this equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

On Rational Functions Sharing the Measure of Maximal Entropy

, Volume 6 (3-4) – Apr 29, 2020
10 pages      /lp/springer-journals/on-rational-functions-sharing-the-measure-of-maximal-entropy-HoMb0Z36Yq
Publisher
Springer Journals
Copyright © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2020
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-020-00141-z
Publisher site
See Article on Publisher Site

Abstract

We show that describing rational functions f1,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f_1,$$\end{document}f2,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f_2,$$\end{document}⋯,fn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\dots ,f_n$$\end{document} sharing the measure of maximal entropy reduces to describing solutions of the functional equation A∘X1=A∘X2=⋯=A∘Xn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A\circ X_1=A\circ X_2=\dots =A\circ X_n$$\end{document} in rational functions. We also provide some results about solutions of this equation.

Journal

Arnold Mathematical JournalSpringer Journals

Published: Apr 29, 2020