<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></p><p class=MsoNormal>School of Mathematics<o:p></o:p></p><p class=MsoNormal>Princeton, NJ 08540<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Members' Seminar<o:p></o:p></p><p class=MsoNormal>Monday, March 18<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>To view mathematics in titles and abstracts, please click on the talk's link.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Topic: Tracking trajectories in Hamiltonian systems using holomorphic curve tools.<o:p></o:p></p><p class=MsoNormal>Speaker: Barney Bramham, Ruhr University Bochum; von Neumann Fellow, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link: </span><a href="http://www.math.ias.edu/seminars/abstract?event=129431"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=129431</span></a><span lang=FR><o:p></o:p></span></p><p class=MsoNormal><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal>The goal is to describe how techniques from symplectic dynamics can be used to study orbit travel in three dimensions, for systems like the restricted 3-body problem from celestial mechanics. The pseudo-holomorphic curve theory initiated by Hofer, Wysocki and Zehnder gives a decomposition of the space into regions whose boundaries are surfaces transverse to the flow. (Pseudo-holomorphic curves are special minimal surfaces). One can label the regions A, B, C etc and form a directed graph. This gives us a natural language to discuss trajectories of orbits, a topic notorious for its complexity. Certain interesting features arise from this structure. I will describe how semi-local considerations lead to more global information and symbolic dynamics. This is joint work with Umberto Hryniewicz and Gerhard Knieper. The talk will address a general mathematical audience.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><a href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a><o:p></o:p></p></div></body></html>