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</o:shapelayout></xml><![endif]--></head><body lang=SL link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Vabimo vas na 21. predavanje iz sklopa "Kolokviji na IJS" v letu 2012/13, ki bo <strong>v sredo, 28. avgusta 2013, ob 13. uri </strong>v Veliki predavalnici Instituta »Jožef Stefan« na Jamovi cesti 39 v Ljubljani. Napovednik predavanja najdete tudi na naslovu <a href="http://www.ijs.si/ijsw/Koledar_prireditev"><span style='color:windowtext'>http://www.ijs.si/ijsw/Koledar_prireditev</span></a>, posnetke preteklih predavanj pa na <a href="http://videolectures.net/kolokviji_ijs"><span style='color:windowtext'>http://videolectures.net/kolokviji_ijs</span></a>. <o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<o:p></o:p></p><p class=MsoNormal><b>dr. Milovan Šuvakov<o:p></o:p></b></p><p class=MsoNormal><i>Institut za fiziko, Beograd, Srbija<o:p></o:p></i></p><p class=MsoNormal><i><o:p> </o:p></i></p><p class=MsoNormal><b><span style='font-size:14.0pt;mso-fareast-language:SL'><o:p> </o:p></span></b></p><p class=MsoNormal style='text-align:justify'><b><span style='font-size:14.0pt'>Newtonov problem treh teles: 13 novih periodičnih rešitev in topološka klasifikacija<o:p></o:p></span></b></p><p class=MsoNormal style='text-align:justify'><span style='font-size:11.0pt;font-family:"Arial","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify'>Problem treh teles sega v l. 1680. Že Isaac Newton je pokazal, da lahko z zakonom težnosti natančno napove orbito dveh teles, ki ju veze težnost, npr. zvezde in planeta. Periodična orbita dveh teles je vselej elipsa (v posebnem primeru krožnica). <o:p></o:p></p><p class=MsoNormal style='text-align:justify'>Dve stoletji so znanstveniki na različne načine skušali najti podobno rešitev za problem treh teles, dokler ni nemški matematik Heinrich Bruns pokazal, da je iskanje splošne rešitve problema treh teles brezplodno in da so mogoče le rešitve, ki se nanašajo na posebne primere. Doslej so bile znane le tri družine breztrkovnih periodičnih orbit: 1) Lagrange-Eulerjeva (1772), 2) Broucke-Hénonova (1975), in Moorova periodična orbita v obliki osmice (1993). Tu poročamo o odkritju 13 novih družin periodičnih orbit, s katerimi število družin naraste na skupaj 16. Predstavimo numerične metode, s katerimi smo jih odkrili in ločili od drugih, ter naslednje korake v raziskavah tega problema (npr. določanje stabilnih novih rešitev, ki ostanejo na tiru tudi, če jih nekoliko perturbiramo). Če je katera od novih rešitev stabilna, jo morda lahko celo opazimo.<i><o:p></o:p></i></p><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt;text-align:justify'>Predavanje bo v angleščini.<span style='mso-fareast-language:SL'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><strong><span style='font-family:"Calibri","sans-serif"'>Lepo vabljeni!</span></strong><strong><span style='font-weight:normal'><o:p></o:p></span></strong></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal align=center style='text-align:center'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>*****<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>We invite you to the 21st Institute colloquium in the</span><span lang=EN-GB style='color:black'> academic</span><span style='color:black'> year 2012/13. The colloquium will be held <b>on Wednesday August 28, 2013 at 1 PM</b> in <b>the main Institute</b></span><b><span style='color:#1F497D'> </span><span style='color:black'>lecture hall</span></b><span style='color:black'>, Jamova 39, Ljubljana. To read the abstract click </span><span style='color:#1F497D'><a href="http://www.ijs.si/ijsw/Koledar_prireditev">http://www.ijs.si/ijsw/Koledar_prireditev</a>. </span><span style='color:black'>Past colloquia are posted on</span><span style='color:#1F497D'> <a href="http://videolectures.net/kolokviji_ijs">http://videolectures.net/kolokviji_ijs</a>.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'>********************************************<b><o:p></o:p></b></p><p class=MsoNormal><b>dr. Milovan Šuvakov<o:p></o:p></b></p><p class=MsoNormal><i>Institute of Physics, Belgrade, Serbia<o:p></o:p></i></p><p class=MsoNormal><b><span style='font-size:16.0pt'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:16.0pt'>The Newtonian three-body problem: 13 new periodic solutions and topological classification</span></b><b><span style='font-size:16.0pt;mso-fareast-language:SL'><o:p></o:p></span></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The three-body problem dates back to the 1680s. Isaac Newton had already shown that his law of gravity could always predict the orbit of two bodies held together by gravity, such as a star and a planet, with complete accuracy. The periodic two-body orbit is always an ellipse (sometimes turning into a circle). For two centuries, scientists tried different tacks to find similar solution for three-body problem, until the German mathematician Heinrich Bruns pointed out that the search for a general solution for the three-body problem was futile, and that only specific solutions that work only under particular conditions, were possible. Only three families of such collisionless periodic orbits were known until recently: 1) the Lagrange-Euler (1772); 2) the Broucke-Hénon (1975); and 3) Cris Moore's (1993) periodic orbit of three bodies moving on a "figure-8" trajectory. We report the discovery of 13 new families of periodic orbits, bringing the new total to 16. We discuss the numerical methods used to find them and distinguish them from others, as well as the next steps in this line of research (e.g. to see how many of the new solutions are stable and will stay on track if perturbed a little). If some of the solutions are stable, then they might even be glimpsed in real life.<o:p></o:p></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p></div></body></html>