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\begin{document}
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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge הסתברות ותורה ארגודית}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום רביעי, 12 ביולי, 2017}
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\textbf{בשעה} \emph{11:00 -- 12:00}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Definition of Chaos In Sense Of Devaney\par}
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תינתן על-ידי
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{\large\scshape Basheer Abu Khalil}
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\textbf{תקציר:}
  Devaney’s definition of chaos is one of the most popular and widely known. A continuous map f from a compact
metric space (X, d) to itself is chaotic in the sense of Devaney if
(1) f is transitive,
(2) the set of all periodic points of f is dense in X, and
(3) f has sensitive dependence on initial conditions.
we will show that  (1) and (2) imply (3) in Devaney’s definition in any metric space. We will show (1) and (3) do not imply (2) 
 and (2) ; (3) do not imply (1).
We will also show that for continuous maps on an interval in R; transitivity implies that the set of periodic points
is dense. It follows that transitivity implies chaos, and we will give some examples to note that there are no other trivialities in Devaney’s definition when restricted to interval.
  


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{\bfseries אנא שימו לב לשינוי ביום ושעה!}
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