Type: Seminar

Distribution: World

Expiry: 17 Jun 2019

CalTitle1: Simultaneous Binary Collisions and the Mysterious 8/3

Auth: erich@10.17.15.2 (ehes5653) in SMS-WASM

Hello all, The next MaPSS talk of this semester will be at 17:00 on Monday 18th March in Carslaw 535. It’s a great opportunity to meet fellow postgrads, listen to an interesting talk, and of course get some free pizza! ************************************************************************************** Speaker: Nathan Duignan Title: Simultaneous Binary Collisions and the Mysterious 8/3 Abstract: Of central importance in the N-body problem is the fact that isolated binary collisions can be regularized : that a singular change of space and time variables (first written down by Levi-Civita) allows trajectories to pass analytically through binary collisions unscathed. The resulting flow is smooth with respect to initial conditions. Curiously, we are not so lucky with simultaneous binary collisions. In a landmark paper, Martinez and Simo gave strong evidence that the best one can hope is 8/3 differentiability of the flow in a neighborhood of simultaneous binary collisions in the 4 body problem. In this talk we follow Easton by linking regularizability to the behaviour of the flow in Conley isolating blocks around the collisions. We show the 8/3 is produced from the first resonant monomial with nonzero coefficient near a degenerate singularity formed when the two binaries are separately Levi-Civita regularized. To show this, we blow-up the singularity and study the flow near the resulting two, 3:1 resonant, normally hyperbolic manifolds connected by heteroclinics. A lengthy normal form computation confirms the conjecture. ************************************************************************************** See you there! Details can also be found on the school’s new Postgraduate Society website: http://www.maths.usyd.edu.au/u/MaPS/mapss.html Cheers, Eric