Topological lower bounds for the Rössler System

The Rössler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. Building on previous work by the author, in this paper we characterize the dynamical complexity for the Rössler System at parameter values at which the flow satisfies a certain heteroclinic condition. This will allow us to characterize the knot type of infinitely many periodic trajectories for the flow - and reduce the Rössler system to a simpler hyperbolic flow, capturing its essential dynamics.