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'hyperbolic fixed point'
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| Title of object: |
hyperbolic fixed point |
| Canonical Name: |
HyperbolicFixedPoint |
| Type: |
Definition |
| Created on: |
2003-07-27 13:05:51 |
| Modified on: |
2003-07-27 13:05:51 |
| Classification: |
msc:37C25, msc:37D05 |
| Defines: |
hyperbolic periodic point |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathrsfs}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\newcommand{\C}{\mathbb{C}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Per}{\operatorname{Per}} |
Content:
Let $M$ be a smooth manifold. A fixed point $x$ of a diffeomorphism
$f\colon M\to M$ is said to be a \textbf{hyperbolic fixed point} if $Df(x)$ is a linear hyperbolic isomorphism. If $x$ is a periodic point of least period $n$, it is called a \textbf{hyperbolic periodic point} if it is a hyperbolic fixed point of $f^n$ (the $n$-th iterate of $f$). |
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