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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
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\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}[theorem]{Definition}
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\begin{document}
\title{Chaos By Instability In Bunched Beam}
\author{V. Zadorozhny}
\address{Institute of Cybernetic, National Academy of Sciences of Ukraine\\
zvf@umex.istrada.net.ua}
\maketitle
\pacs{23.23+x,56,65.}

\begin{abstract}
Chaos is the best known for a paper written almost 30 years ago. The basic
tenet of the theory is that, for a given system, a tiny change in starting
conditions can have a profound effect on end results. The deterministic
chaos has both captured the integrability and instability dynamical systems.
In the last year, chaos has been sought as a tool to resolve apparent
uncertainties in the material world (M.Peel).

Using the self selfconsistent Vlasov equation we discuss a wave dynamical
system to describe the chaotic behavior of the bunched beam, present some
results of the existence of the global solutions at the generalized
functions. \ Disappearance of the first integral and \ appearance of the
wave packet chaos as a result of birth of the continuous \ spectrum in
Vlasov system is studied. We proposed a new concept of wave packet chaos to
describe the chaotic behavior of the wave dynamical system.
\end{abstract}

\end{document}