hmacro.tex


 
\def\present#1{\noindent{\bf#1}}                     %Eric's version of give.
\outer\def\give#1. {\medbreak
             \noindent{\bf#1. }}                     %introduces proofs etc.
\outer\def\section #1\par{\bigbreak\centerline{\S
     {\bf#1}}\nobreak\smallskip\noindent}
\def\({\left(}
\def\){\right)}
\def\contract{{\,{\vrule height5pt width0.4pt depth 0pt}
{\vrule height0.4pt width6pt depth 0pt}\,}}
 
\def\wedgedot{\mathrel{\mathop\wedge^{\bf.}}}
\def\sqr#1#2{{\vcenter{\hrule height.#2pt              %qed
     \hbox{\vrule width.#2pt height#1pt\kern#1pt
     \vrule width.#2pt}
     \hrule height.#2pt}}}
\def\square{\mathchoice\sqr{5.5}4\sqr{5.0}4\sqr{4.8}3\sqr{4.8}3}
\def\qed{\hskip4pt plus1fill\ $\square$\par\medbreak}
  


%section 1
\def\He{H\'enon}
\def\HO{Hubbard and Oberste-Vorth}
 
%section 2
\def\xy{{x\choose y}}
\def\fto#1{f^{(#1)}}
 
 
%section 4
\def\cA{{\cal A}}
\def\cB{{\cal B}}
\def\cC{{\cal C}}
\def\cD{{\cal D}}
\def\cE{{\cal E}}
\def\cF{{\cal F}}
\def\cG{{\cal G}}
\def\cH{{\cal H}}
\def\cI{{\cal I}}
\def\cJ{{\cal J}}
\def\cK{{\cal K}}
\def\cL{{\cal L}}
\def\cM{{\cal M}}
\def\cN{{\cal N}}
\def\cO{{\cal O}}
\def\cP{{\cal P}}
\def\cQ{{\cal Q}}
\def\cR{{\cal R}}
\def\cS{{\cal S}}
\def\cT{{\cal T}}
\def\cU{{\cal U}}
\def\cV{{\cal V}}
\def\cW{{\cal W}}
\def\cX{{\cal X}}
\def\cY{{\cal Y}}
\def\cZ{{\cal Z}}
 
 
 
%general
 
\def\CC{{\rm\kern.24em\vrule width.02em height1.4ex depth-.05ex\kern-.26em C}}
\def\RR{{\,\rm{\vrule width.02em height1.55ex depth-.07ex\kern-.3165em R}}}


\def\complex{{{\bf C}}}     % complex numbers
\def\C{{\bf C}}
\def\cx#1{{\C}^{#1}}     % C to power n
\def\cp1{{{\bf P}^1}}
\def\reals{{\RR}}         % real numbers
\def\R{{\bf R}}
\def\real#1{{\bf R}^{#1}}   % R to power n
\def\ints{{\bf Z}}          % integers
\def\ball#1{{\bf B}^{#1}}   % ball of dimension n
\def\cball#1{\overline{{\bf B}}^{#1}}
\def\Z{{\bf Z}}
\def\Q{{\bf Q}}
                                 % closed n-ball
\def\re{\it{\,Re\,}}		 % real part
\def\im{\it{\,Im\,}}		 % imaginary part
\def\bar{\overline}              % conjugate
\def\smooth#1{{\cal C}^{#1}}     % smooth of order #1
\def\ts{{\it T}}            % tangent space, roman T
\def\bs{\backslash}              % backslash
\def\abs#1{|#1|}                 % absolute value
 
\def\disc{\triangle}             % disc
\def\disk{\triangle}             % disk
\def\intr{{\rm\,int\,}}		 % interior, in math mode
 
\def\di{\partial}                % partial derivative
\def\bd{\partial}		 % boundary (same thing)
 
 
%\def\nbd{neighborhood\ }         % neighborhood
%\def\vec#1#2{({#1}_1,\dots,{#1}_{#2})}
				 % vector of #1 of length #2
%\def\inner#1#2{\langle{#1},{#2}\rangle}  % inner product

