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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the fixed point index of iterates of planar homeomorphisms
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by Morton Brown
Proc. Amer. Math. Soc. 108 (1990), 1109-1114
DOI: https://doi.org/10.1090/S0002-9939-1990-0994772-9

Abstract:

If $f$ is an orientation preserving homeomorphism of the plane with an isolated fixed point at the origin 0 and ${\text {index(}}f,0{\text {) = }}p$, then ${\text {index(}}{f^n}{\text {,0)}}$ is always well defined provided that $p \ne 1$. In this case, for each $n \ne 0$, ${\text {index(}}{f^n}{\text {,0) = index(}}f,o{\text {) = }}p$. If ${\text {index(}}f,0{\text {) = 1}}$, then there is an integer $p$ (possibly $p = 1$) such that for those values of $n$ for which ${\text {index(}}{f^n}{\text {,0)}}$ is defined (i.e 0 is an isolated fixed point of ${f^n}$), ${\text {index(}}{f^n}{\text {,0) = 1}}$ or ${\text {index(}}{f^n}{\text {,0) = }}p$.
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Bibliographic Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 1109-1114
  • MSC: Primary 54H25; Secondary 55M20, 55M25, 57N05
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0994772-9
  • MathSciNet review: 994772