Can Morse trajectories break if their first derivative is uniformly bounded? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T03:04:53Z http://mathoverflow.net/feeds/question/55711 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/55711/can-morse-trajectories-break-if-their-first-derivative-is-uniformly-bounded Can Morse trajectories break if their first derivative is uniformly bounded? Orbicular 2011-02-17T09:23:12Z 2011-02-17T09:23:12Z <p>Consider a compact Riemannian manifold endowed with a Morse function f. Fix two critical points x and y of f. Whenever you have a sequence \$u_k\$ of Morse trajectories connecting x and y it might happen that the \$u_k\$ "converge" to a broken trajectory. Suppose there is a bound \$\|u_k'(s)\|\le C\$ independently of k and s. Can the sequence still break?</p>