<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-9">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:#000000; font-family:Calibri,Arial,Helvetica,sans-serif">
<p><br>
</p>
<p></p>
<p class="MsoNormal"><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Sayin Liste Uyeleri,<br>
<br>
Gebze Teknik Üniversitesi (GTU</span>) <span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">
Matematik Bölümü Genel Seminerleri kapsamında,<br>
9 Aralık Cuma günü saat 14:00'da </span>Ayşegül Kıvılcım<span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"> (İstanbul
Aydın Üniversitesi) bir seminer verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.<br>
<br>
Saygılarımızla.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"><br>
Dear all,<br>
<br>
There will be a seminar in Gebze Technical University (GTU) on 9th of<br>
December by Ayşegül Kıvılcım </span><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">(Istanbul
Aydın University)<br>
Time and place: At 14:00 in Department of Mathematics, Building I, Seminar room.<br>
<br>
Title: <span style="font-size: 12pt;">Discontinuous dynamics with grazing points</span><br>
<br>
Abstract:<!--[endif]--> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"></p>
<pre style="margin-top: 0px; margin-bottom: 0px;">Discontinuous dynamical systems with grazing solutions are discussed. </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">The group property, continuation of solutions, continuity and smoothness </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">of motions are thoroughly <span style="text-decoration: underline;">analyzed</span>. A variational system around a grazing </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">solution which depends on near solutions is constructed. Orbital</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> stability of grazing cycles is examined by <span style="text-decoration: underline;">linearization</span>. Small</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> parameter method is extended for analysis of <span style="text-decoration: underline;">neighborhoods</span> of </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">grazing orbits, and grazing bifurcation of cycles is observed </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">in an example. <span style="text-decoration: underline;">Linearization</span> around an equilibrium grazing point </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">is discussed. The mathematical background of the study relies</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> on the theory of discontinuous dynamical systems [1]. Our approach</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> is analogous to that one of the continuous dynamics analysis and results</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> can be extended on functional differential, partial differential equations </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">and others. Appropriate illustrations with grazing limit cycles and </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">bifurcations are depicted to support the theoretical results. </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">As an example, a coupled Van <span style="text-decoration: underline;">der</span> <span style="text-decoration: underline;">Pol</span> oscillators with impacts </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">is taken into account. In addition to these results, non-autonomous </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">grazing phenomenon is investigated through periodic systems and their </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">solutions. The analysis is different than for autonomous systems </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">in many aspects. Conditions for the existence of a <span style="text-decoration: underline;">linearization</span> </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">have been found. Stability of a periodic solution and its persistence</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"> under regular perturbations are investigated. Through examples, </pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">the theoretical results are visualized. </pre>
<br>
</span>
<p></p>
<p></p>
<div id="Signature">
<div id="divtagdefaultwrapper" style="font-size:12pt; color:#000000; background-color:#FFFFFF; font-family:Calibri,Arial,Helvetica,sans-serif">
<p></p>
</div>
</div>
</div>
</body>
</html>