llncs.tex

是一个将WORD文件转换成TXT文件的程序源代码

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With this chapter, the preliminaries are over, and we begin the

\noindent
search for periodic solutions $\backslash $dots

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$\backslash $subsection{\{}Autonomous Systems{\}}

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In this section we will consider the case when the Hamiltonian

{\$}H(x){\$} $\backslash $dots

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$\backslash $subsubsection*{\{}The General Case: Nontriviality.{\}}

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We assume that {\$}H{\$} is

{\$}$\backslash $left(A{\_}{\{}$\backslash $infty{\}}, B{\_}{\{}$\backslash 
$infty{\}}$\backslash $right){\$}-subqua$\backslash $-dra$\backslash $-tic

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at infinity, for some constant $\backslash $dots

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$\backslash $paragraph{\{}Notes and Comments.{\}}

The first results on subharmonics were $\backslash $dots

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$\backslash $begin{\{}proposition{\}}

Assume {\$}H'(0)=0{\$} and {\$} H(0)=0{\$}. Set $\backslash $dots

$\backslash $end{\{}proposition{\}}

$\backslash $begin{\{}proof{\}}[of proposition]

Condition (8) means that, for every {\$}$\backslash $delta'>$\backslash 
$delta{\$}, there is

\noindent
some {\$}$\backslash $varepsilon>0{\$} such that $\backslash $dots 
$\backslash $qed

$\backslash $end{\{}proof{\}}

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$\backslash $begin{\{}example{\}}[$\backslash $rmfamily (External forcing)]

Consider the system $\backslash $dots

$\backslash $end{\{}example{\}}

$\backslash $begin{\{}corollary{\}}

Assume {\$}H{\$} is {\$}C\ {\{}2{\}}{\$} and

{\$}$\backslash $left(a{\_}{\{}$\backslash $infty{\}}, b{\_}{\{}$\backslash 
$infty{\}}$\backslash $right){\$}-subquadratic

\noindent
at infinity. Let $\backslash $dots

$\backslash $end{\{}corollary{\}}

$\backslash $begin{\{}lemma{\}}

Assume that {\$}H{\$} is {\$}C\ {\{}2{\}}{\$} on {\$}$\backslash 
$bbbr\ {\{}2n{\}}$\backslash $backslash $\backslash ${\{}0$\backslash 
${\}}{\$}

\noindent
and that {\$}H''(x){\$} is $\backslash $dots

$\backslash $end{\{}lemma{\}}

$\backslash $begin{\{}theorem{\}}[(Ghoussoub-Preiss)]

Let {\$}X{\$} be a Banach Space and {\$}$\backslash $Phi:X$\backslash 
$to$\backslash $bbbr{\$} $\backslash $dots

$\backslash $end{\{}theorem{\}}

$\backslash $begin{\{}definition{\}}

We shall say that a {\$}C\ {\{}1{\}}{\$} function {\$}$\backslash 
$Phi:X$\backslash $to$\backslash $bbbr{\$}

\noindent
satisfies $\backslash $dots

$\backslash $end{\{}definition{\}}

$\backslash $end{\{}verbatim{\}}

{\{}$\backslash $itshape Sample Output$\backslash $/{\}} (follows on the 
next page together with

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examples of the above run-in headings)

$\backslash $newcounter{\{}save{\}}$\backslash 
$setcounter{\{}save{\}}{\{}$\backslash $value{\{}section{\}}{\}}

{\{}$\backslash $def$\backslash $addtocontents{\#}1{\#}2{\{}{\}}{\%}

$\backslash $def$\backslash $addcontentsline{\#}1{\#}2{\#}3{\{}{\}}{\%}

$\backslash $def$\backslash $markboth{\#}1{\#}2{\{}{\}}{\%}

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$\backslash $title{\{}Hamiltonian Mechanics{\}}



$\backslash $author{\{}Ivar Ekeland$\backslash $inst{\{}1{\}} $\backslash $and 
Roger Temam$\backslash $inst{\{}2{\}}{\}}



$\backslash $institute{\{}Princeton University, Princeton NJ 08544, USA

$\backslash $and

Universit$\backslash $'{\{}e{\}} de Paris-Sud,

Laboratoire d'Analyse Num$\backslash $'{\{}e{\}}rique, B$\backslash 
$\ {\{}a{\}}timent 425,$\backslash \backslash $

F-91405 Orsay Cedex, France{\}}



$\backslash $maketitle

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$\backslash $begin{\{}abstract{\}}

This paragraph shall summarize the contents of the paper

\noindent
in short terms.

$\backslash $end{\{}abstract{\}}

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$\backslash $section{\{}Fixed-Period Problems: The Sublinear Case{\}}

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With this chapter, the preliminaries are over, and we begin the search

\noindent
for periodic solutions $\backslash $dots

{\%}

$\backslash $subsection{\{}Autonomous Systems{\}}

{\%}

In this section we will consider the case when the Hamiltonian

{\$}H(x){\$} $\backslash $dots

{\%}

$\backslash $subsubsection{\{}The General Case: Nontriviality.{\}}

{\%}

We assume that {\$}H{\$} is

{\$}$\backslash $left(A{\_}{\{}$\backslash $infty{\}}, B{\_}{\{}$\backslash 
$infty{\}}$\backslash $right){\$}-subqua$\backslash $-dra$\backslash $-tic 
at

\noindent
infinity, for some constant $\backslash $dots

{\%}

$\backslash $paragraph{\{}Notes and Comments.{\}}

The first results on subharmonics were $\backslash $dots

{\%}

$\backslash $begin{\{}proposition{\}}

Assume {\$}H'(0)=0{\$} and {\$} H(0)=0{\$}. Set $\backslash $dots

$\backslash $end{\{}proposition{\}}

$\backslash $begin{\{}proof{\}}[of proposition]

Condition (8) means that, for every {\$}$\backslash $delta'>$\backslash 
$delta{\$}, there is

\noindent
some {\$}$\backslash $varepsilon>0{\$} such that $\backslash $dots 
$\backslash $qed

$\backslash $end{\{}proof{\}}

{\%}

$\backslash $begin{\{}example{\}}[{\{}{\{}$\backslash $rmfamily External 
forcing{\}}{\}}]

Consider the system $\backslash $dots

$\backslash $end{\{}example{\}}

$\backslash $begin{\{}corollary{\}}

Assume {\$}H{\$} is {\$}C\ {\{}2{\}}{\$} and

{\$}$\backslash $left(a{\_}{\{}$\backslash $infty{\}}, b{\_}{\{}$\backslash 
$infty{\}}$\backslash $right){\$}-subquadratic

\noindent
at infinity. Let $\backslash $dots

$\backslash $end{\{}corollary{\}}

$\backslash $begin{\{}lemma{\}}

Assume that {\$}H{\$} is {\$}C\ {\{}2{\}}{\$} on {\$}$\backslash 
$bbbr\ {\{}2n{\}}$\backslash $backslash $\backslash ${\{}0$\backslash 
${\}}{\$}

\noindent
and that {\$}H''(x){\$} is $\backslash $dots

$\backslash $end{\{}lemma{\}}

$\backslash $begin{\{}theorem{\}}[Ghoussoub-Preiss]

Let {\$}X{\$} be a Banach Space and {\$}$\backslash $Phi:X$\backslash 
$to$\backslash $bbbr{\$} $\backslash $dots

$\backslash $end{\{}theorem{\}}

$\backslash $begin{\{}definition{\}}

We shall say that a {\$}C\ {\{}1{\}}{\$} function {\$}$\backslash 
$Phi:X$\backslash $to$\backslash $bbbr{\$} satisfies $\backslash $dots

$\backslash $end{\{}definition{\}}

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{\}}$\backslash $setcounter{\{}section{\}}{\{}$\backslash 
$value{\{}save{\}}{\}}

$\backslash $section{\{}Fine Tuning of the Text{\}}

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The following should be used to improve the readability of the text:

$\backslash $begin{\{}flushleft{\}}

$\backslash $begin{\{}tabular{\}}{\{}@{\{}{\}}p{\{}.19$\backslash 
$textwidth{\}}p{\{}.79$\backslash $textwidth{\}}{\}}

$\backslash $verb$\vert \backslash $,$\vert $ {\&} a thin space, 
e.g.$\backslash $ between numbers or between units

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and num$\backslash $-bers; a line division will not be made

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following this space$\backslash \backslash $

$\backslash $verb$\vert $--$\vert $ {\&} en dash; two strokes, without a space 
at either end$\backslash \backslash $

$\backslash $verb*$\vert $ -- $\vert ${\&} en dash; two strokes, with a space 
at either end$\backslash \backslash $

$\backslash $verb$\vert -\vert $ {\&} hyphen; one stroke, no space at either 
end$\backslash \backslash $

$\backslash $verb$\vert ${\$}-{\$}$\vert $ {\&} minus, in the text 
{\{}$\backslash $em only{\}} $\backslash \backslash $[8mm]

{\{}$\backslash $em Input{\}} {\&} $\backslash $verb$\vert $21$\backslash 
$,{\$}\ {\{}$\backslash $circ{\}}{\$}C etc.,$\vert \backslash 
\backslash $

{\&} $\backslash $verb$\vert $Dr h.$\backslash $,c.$\backslash 
$,Rockefellar-Smith $\backslash $dots$\vert \backslash \backslash $

{\&} $\backslash $verb$\vert $20,000$\backslash $,km and Prof.$\backslash 
$,Dr Mallory $\backslash $dots$\vert \backslash \backslash $

{\&} $\backslash $verb$\vert $1950--1985 $\backslash $dots$\vert 
\backslash \backslash $

{\&} $\backslash $verb$\vert $this -- written on a computer -- is now 
printed$\vert \backslash \backslash $

{\&} $\backslash $verb$\vert ${\$}-30{\$}$\backslash $,K $\backslash 
$dots$\vert \backslash \backslash $[3mm]

{\{}$\backslash $em Output{\}}{\&} 21$\backslash $,{\$}\ {\{}$\backslash 
$circ{\}}{\$}C etc., Dr h.$\backslash $,c.$\backslash $,Rockefellar-Smith 
$\backslash $dots$\backslash \backslash $

{\&} 20,000$\backslash $,km and Prof.$\backslash $,Dr Mallory $\backslash 
$dots$\backslash \backslash $

{\&} 1950--1985 $\backslash $dots$\backslash \backslash $

{\&} this -- written on a computer -- is now printed$\backslash \backslash 
$

{\&} {\$}-30{\$}$\backslash $,K $\backslash $dots

$\backslash $end{\{}tabular{\}}

$\backslash $end{\{}flushleft{\}}

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$\backslash $section {\{}Special Typefaces{\}}

{\%}

Normal type (roman text) need not be coded. {\{}$\backslash $itshape 
Italic{\}}

($\backslash $verb$\vert ${\{}$\backslash $em <text>{\}}$\vert $ better 
still $\backslash $verb$\vert \backslash $emph{\{}<text>{\}}$\vert )$ or, 
if

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necessary, {\{}$\backslash $bfseries boldface{\}} should be used for 
emphasis.$\backslash \backslash $[6pt]

$\backslash $begin{\{}minipage{\}}[t]{\{}$\backslash $textwidth{\}}

$\backslash $begin{\{}flushleft{\}}

$\backslash $begin{\{}tabular{\}}{\{}@{\{}{\}}p{\{}.25$\backslash 
$textwidth{\}}@{\{}$\backslash $hskip6pt{\}}p{\{}.73$\backslash 
$textwidth{\}}@{\{}{\}}{\}}

$\backslash $verb$\vert ${\{}$\backslash $itshape Text{\}}$\vert $ {\&} 
{\{}$\backslash $itshape Italicized Text{\}}$\backslash \backslash $[2pt]

$\backslash $verb$\vert ${\{}$\backslash $em Text{\}}$\vert $ {\&} 
{\{}$\backslash $em Emphasized Text --

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if you would like to emphasize a {\{}$\backslash $em definition{\}} within 
an

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italicized text (e.g.$\backslash $ of a {\{}$\backslash $em theorem){\}} you 
should code the

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expression to be emphasized by{\}} $\backslash $verb$\vert \backslash 
$em$\vert $.$\backslash \backslash $[2pt]

$\backslash $verb$\vert ${\{}$\backslash $bfseries Text{\}}$\vert ${\&} 
{\{}$\backslash $bfseries Important Text{\}}$\backslash \backslash $[2pt]

$\backslash $verb$\vert \backslash $vec{\{}Symbol{\}}$\vert $ {\&} Vectors 
may only appear in math mode. The default

$\backslash $LaTeX{\{}{\}} vector symbol has been adapted$\backslash 
$footnotemark$\backslash $

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to LLNCS conventions.$\backslash \backslash $[2pt]

{\&} $\backslash $verb$\vert ${\$}$\backslash $vec{\{}A $\backslash $times 
B$\backslash $cdot C{\}}$\vert $ yields {\$}$\backslash $vec{\{}A$\backslash 
$times B$\backslash $cdot C{\}}{\$}$\backslash \backslash $

{\&} $\backslash $verb$\vert ${\$}$\backslash $vec{\{}A{\}}\ {\{}T{\}} 
$\backslash $otimes $\backslash $vec{\{}B{\}} $\backslash $otimes$\vert 
\backslash \backslash $

{\&} $\backslash $verb$\vert \backslash $vec{\{}$\backslash 
$hat{\{}D{\}}{\}}{\$}$\vert $yields {\$}$\backslash 
$vec{\{}A{\}}\ {\{}T{\}} $\backslash $otimes $\backslash $vec{\{}B{\}} 
$\backslash $otimes

$\backslash $vec{\{}$\backslash $hat{\{}D{\}}{\}}{\$}

$\backslash $end{\{}tabular{\}}

$\backslash $end{\{}flushleft{\}}

$\backslash $end{\{}minipage{\}}



$\backslash $footnotetext{\{}If you absolutely must revive the original 
$\backslash $LaTeX{\{}{\}}

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design of the vector symbol (as an arrow accent), please specify the

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option $\backslash $texttt{\{}[orivec]{\}} in the $\backslash 
$texttt{\{}documentclass{\}} line.{\}}

$\backslash $newpage

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$\backslash $section {\{}Footnotes{\}}

{\%}

Footnotes within the text should be coded:

$\backslash $begin{\{}verbatim{\}}

$\backslash $footnote{\{}Text{\}}

$\backslash $end{\{}verbatim{\}}

{\{}$\backslash $itshape Sample Input{\}}

$\backslash $begin{\{}flushleft{\}}

Text with a footnote$\backslash $verb$\vert \backslash $footnote{\{}The 
$\vert ${\{}$\backslash $tt footnote is automatically

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numbered.{\}}$\backslash $verb$\vert ${\}}$\vert $ and text continues 
$\backslash $dots

$\backslash $end{\{}flushleft{\}}

{\{}$\backslash $itshape Sample Output{\}}

$\backslash $begin{\{}flushleft{\}}

Text with a footnote$\backslash $footnote{\{}The footnote is automatically 
numbered.{\}}

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and text continues $\backslash $dots

$\backslash $end{\{}flushleft{\}}

{\%}

$\backslash $section {\{}Lists{\}}

{\%}

Please code lists as described below:$\backslash \backslash $[2mm]

{\{}$\backslash $itshape Sample Input{\}}

$\backslash $begin{\{}verbatim{\}}

$\backslash $begin{\{}enumerate{\}}

$\backslash $item First item

$\backslash $item Second item

$\backslash $begin{\{}enumerate{\}}

$\backslash $item First nested item

$\backslash $item Second nested item

$\backslash $end{\{}enumerate{\}}

$\backslash $item Third item

$\backslash $end{\{}enumerate{\}}

$\backslash $end{\{}verbatim{\}}

{\{}$\backslash $itshape Sample Output{\}}

$\backslash $begin{\{}enumerate{\}}

$\backslash $item First item

$\backslash $item Second item

$\backslash $begin{\{}enumerate{\}}

$\backslash $item First nested item

$\backslash $item Second nested item

$\backslash $end{\{}enumerate{\}}

$\backslash $item Third item

$\backslash $end{\{}enumerate{\}}

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$\backslash $section {\{}Figures{\}}

{\%}

Figure environments should be inserted after (not in)

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the paragraph in which the figure is first mentioned.

They will be numbered automatically.



Preferably the images should be enclosed as PostScript files -- best as

EPS data using the epsfig package.





If you cannot include them into your output this way and use other

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techniques for a separate production,

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the figures (line drawings and those containing halftone inserts

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as well as halftone figures) {\{}$\backslash $em should not be pasted into 
your

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