BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:J.D. Mireles James (Florida Atlantic University\, USA) DTSTART:20210302T150000Z DTEND:20210302T160000Z DTSTAMP:20260423T024751Z UID:CRM-CAMP/42 DESCRIPTION:Title: Boundary value problems and transversality in conservative systems: comp uter assisted proofs of connection and collision orbits\nby J.D. Mirel es James (Florida Atlantic University\, USA) as part of CRM CAMP (Computer -Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\nAbstract\nI'll d iscuss a framework for two-point boundary value problems in conservative s ystems which detects transversality\, allows for the possibility of multip le changes of coordinates\, and leads naturally to computer assisted proof s. The set-up applies to dynamical problems in the level set like finding connecting orbits between hyperbolic invariant objects and collisions. T he main technical difficulty is that the conserved quantity leads to overd etermined systems of equations. This problem can be overcome in a number of different ways\, including elimination of an equation\, by exploiting d iscrete symmetries (if any)\, or by introducing a new variable called an u nfolding parameter. I'll look at two common ways of defining unfolding p arameters and show that they don't disrupt the transversality properties o f the BVP. I'll also illustrate some applications of this setup to comput er assisted proofs of connecting orbits and collisions in the circular res tricted three body problem. This is joint work with Shane Kepley and Maci ej Capinski.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/42/ END:VEVENT END:VCALENDAR