Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift–Hohenberg Equation

Jan Bouwe van den Berg, Jean-Philippe Lessard
2008 SIAM Journal on Applied Dynamical Systems  
We prove that the stationary Swift-Hohenberg equation has chaotic dynamics on a critical energy level for a large (continuous) range of parameter values. The first step of the method relies on a computer assisted, rigorous, continuation method to prove the existence of a periodic orbit with certain geometric properties. The second step is topological: we use this periodic solution as a skeleton, through which we braid other solutions, thus forcing the existence of infinitely many braided
more » ... c orbits. A semi-conjugacy to a subshift of finite type shows that the dynamics is chaotic.
doi:10.1137/070709128 fatcat:2atmooxf3nbhtpcblzo7vecc4u