This scientist discovered structures where the stable and unstable manifolds of a fixed point intersect infinitely called homoclinic tangles. Élie Cartan (“ay-LEE car-TAWN”) used differential forms to express this scientist’s integral invariants, one of which requires the sum of the oriented areas of projections onto canonical planes to be preserved. After discovering an error in his own work, this scientist paid to recall his paper that had won a prize awarded by King Oscar II (“the second”). This scientist proved that a Hamiltonian system with a finite phase space volume will return arbitrarily close to its initial state infinitely many times. The state space of a dynamical system can be visualized with this scientist’s namesake sections. This scientist names the group of isometries of Minkowski (“min-KOF-skee”) spacetime. For 10 points, every simply connected, closed 3-manifold is homeomorphic to the 3-sphere by what French mathematician’s conjecture? ■END■
ANSWER: Henri Poincaré (“awn-REE pwahn-kah-RAY”) [accept Poincaré conjecture; accept Poincaré group; accept Poincaré sections; accept Poincaré recurrence theorem; accept Poincaré–Cartan integral invariants]
<Physics>
= Average correct buzz position